Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2024-25
Module Leader
Lab Leader
Timing and Structure
Michaelmas term. In-person lectures and demonstrations. Coursework with integrated lectures. Assessment: 100% coursework.
Prerequisites
3A1 and 3A3 assumed. Pre-module reading about Fortran helpful
Aims
The aims of the course are to:
- Provide an introduction to the field of computational fluid mechanics.
- Develop an understanding of how numerical techniques are devised.
- Implement these techniques in a practical computer program.
- Overview the nature of simulation in the future and advanced methods.
Objectives
As specific objectives, by the end of the course students should be able to:
- Formulate numerical approximations to partial differential equations.
- Write computer programs for solving the resulting difference equations and processing their solutions.
- Learn about modern methods to improve simulation accuracy.
- Appreciate the capabilities of numerical methods to predict complex flows.
Content
This is a coursework based project. The students write a Computational Fluid Dynamics (CFD) program to solve the Euler equations in 2D with time marching. There are also some basic mesh generation, pre-processing and post-processing tasks. The assessment is through two reports: The first report demonstrates the performance of a basic CFD program and studies basic properties of finite differencing methods. This is to be submitted in Week 6 of the Michaelmas term. The 2nd report demonstrates the coding and performance of more advanced CFD algorithms with discussion on a selected advanced CFD topic. The performance and traits of the extended CFD code are contrasted with expected traits for a range of subsonic, transonic and supersonic flows. The final report is submitted after the end of the Michaelmas term in Week 10.
Writing a CFD Solver and Numerical Concepts (5L)
- The proper use of CFD and the equations used for compressible flows
- Finite difference, finite volume, finite element approaches
- Program specification and structure
- Difference schemes, stability, dispersion and diffusion errors
- Turbulence modelling, adaptive methods, multi-phase flows and parallel computing
- Hyperbolicity and the upwinding method for advection
- Total variation diminishing (TVD) methods
Coursework
Brief Progress Check Report / Week 6 of Michaelmas term [25%]
Complete Final Report / Week 10 after end of Michaelmas term [75%]
The entire module is expected to take around 80 hours, similar to other exam based modules. It includes:
- 5 hours of lectures
- Approximately 50 hours of demonstrated sessions, you are not expected to attend all and attendance is not recorded
- Report writing
The demonstrated sessions will help you with:
- Examples of basic Fortran programs
- Mesh generation for simplified geometries
- Constructing an initial flowfield guess
- Finite volume discretisation, evaluation of fluxes
- Application of boundary conditions
- Time marching, simple LAX method
- Convergence & accuracy testing
- Solver enhancements to investigate a choice of challenging test cases
- Post-processing to produce final report data
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 / Interim] Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
Thu week 6 [25%] |
|
[Coursework activity #2 / Final] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
Wed week 10 [75%] |
Booklists
Main course text is:
LeVeque R. J. 2002. Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.
Also, useful material can be found in these texts:
Ferziger J. H. and Peric M. 2002. Computational Methods for Fluid Dynamics, Springer.
Toro E. F. 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer
Hirsch C. 1988-1990 Numerical Computation of Internal and External Flows, Volumes 1 and 2, Wiley
Davies R., Rea A. and Tsaptsinos D. Introduction to FORTRAN 90, Student Notes, Queen's University, Belfast
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
Knowledge and Understanding
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 09/10/2024 21:08
Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2020-21
Module Leader
Lecturer
Dr J Li
Lab Leader
Dr J Li
Timing and Structure
Michaelmas term. Online lectures and demonstrations. Coursework with integrated lectures. Assessment: 100% coursework.
Prerequisites
3A1 and 3A3 assumed. Pre-module reading about Fortran helpful
Aims
The aims of the course are to:
- provide an introduction to the field of computational fluid mechanics.
- help students develop an understanding of how numerical techniques are devised.
- implement these techniques in practical computer codes.
- overview the nature of simulation in the future and advanced methods.
Objectives
As specific objectives, by the end of the course students should be able to:
- formulate numerical approximations to partial differential equations.
- write computer programs for solving the resulting difference equations.
- learn modern TVD shock-capturing methods.
- appreciate the power of numerical solutions to predict complex flows, including shock waves.
- develop the critical skills necessary to respond to and audit simulations produced by CFD for complex flow problems.
Content
This is a course work based project. The students have to write a Computational Fluid Dynamics (CFD) program - in Euler mode with time marching. There is also some basic mesh generation, preprocessing and post processing tasks. The assessment is through two reports. The first report demonstrates the performance of a basic CFD program and studies basic properties of finite difference methods. This needs to be handed in week 6 of the Michaelmas term. The 2nd report demonstrates the coding and performance of more advanced CFD algorithms with discussion on a selected advanced CFD topic. The performance and traits of the extended CFD code are contrasted with expected traits for a range of subsonic and transonic flows. The final report is handed in at the end of the Michaelmas term.
Introduction and Basic Numerical Concepts (2L)
- The proper use of CFD and the equations used
- Finite difference, finite volume, finite element approaches
- Difference scheme and molecules
- Stability, Dispersion and Diffusion errors, Cell Re
- Compressible Flows vs Incompressible Flows
- Single Phase Flows vs Multiphase Flows
- Turbulence Modelling, Adaptive Methods and Parallel Computing
Modern Shock-Capturing Methods for Time-Dependent Compressible Flows (6L)
- Euler Equations and Hyperbolicity
- The Upwinding Method for Advection
- Godunov's Method for Linear System
- Total Variation Diminishing (TVD) Methods
- High-Resolution Methods and Limiters
- Approximate Riemann Solvers
- Roe Solver for Euler Equations
Coursework
Progress Check/Brief Report/Week 6 of Michaelmas term [25%]
Coursework/Report/1 Week after end of Michaelmas term [75%]
Mesh Generation and Preprocessing (Coursework: approx 2 hours)
- Conversion to Fortran; examples of Fortran programs
- Mesh generation for simplified geometries (eg bend, nozzle, hump, airfoil)
- Preprocessing
2-D Euler, Time Marching CFD Program
(Coursework: 5 mini-exercises of about 2-4 hours each, forming a 16 hour mini-project)
- Finite volume discretisation, evaluation of fluxes. (4h)
- Application of boundary conditions. (2h)
- Time Iteration, simple LAX method. (2h)
- Convergence & accuracy testing. (4h)
- Enhancements, e.g. deferred corrections, Adams - Bashforth RK integration, use of energy equation. (4h)
- Exploration of post-processing
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 title / Interim] Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
day during term, ex: Thu week 6 [25%] |
|
[Coursework activity #2 title / Final] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
Fri week 10 [75%] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Main course text is:
LeVeque R. J. 2002. Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.
Also, useful material can be found in these texts.
Ferziger J. H. and Peric M. 2002. Computational Methods for Fluid Dynamics, Springer.
Toro E. F. 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer
Hirsch C. 1988-1990 Numerical Computation of Internal and External Flows, Volumes 1 and 2, Wiley
Davies R., Rea A. and Tsaptsinos D. Introduction to FORTRAN 90, Student Notes, Queen's University, Belfast
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 13/09/2020 21:17
Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2018-19
Module Leader
Lecturer
Dr T P Hynes
Lab Leader
Timing and Structure
Michaelmas term. Coursework with integrated lectures. Assessment: 100% coursework.
Prerequisites
3A1 and 3A3 assumed. Pre-module reading about Fortran helpful
Aims
The aims of the course are to:
- provide an introduction to the field of computational fluid mechanics.
- help students develop an understanding of how numerical techniques are devised and analysed with solution of fluid flow problems as the target.
- provide some experience in the software engineering skills associated with the implementation of these techniques in practical computer codes.
- illuminate some of the difficulties encountered in the numerical solution of fluid flow problems.
- Overview the nature of simulation in the future and advanced methods relating to this
Objectives
As specific objectives, by the end of the course students should be able to:
- formulate numerical approximations to partial differential equations.
- write computer programs for solving the resulting difference equations.
- understand the limitations of numerical methods and the compromises between accuracy and mean time.
- appreciate the power of numerical solutions to predict complex flows, including shock waves.
- develop the critical skills necessary to respond to and audit simulations produced by CFD for complex flow problems.
Content
This is a course work based project. The students have to write a Computational Fluid Dynamics (CFD) program - in Euler mode with time marching. There is also some basic mesh generation, preprocessing and post processing tasks. The assessment is through two reports. The first report demonstrates the performance of a basic CFD program and some discussion on general aspects of CFD. This needs to be handed in week 6 of the Michaelmas term. The 2nd report demonstrates the coding and performance of more advanced CFD algorithms with discussion on a selected advanced CFD topic. The performance and traits of the extended CFD code are contrasted with expected traits for a range of subsonic and transonic flows. The final report is handed in at the end of the Michaelmas term. The course also allows for some creativity through the design of novel algorithmic approaches.
Introduction and Basic Numerical Concepts (2L including examples, plus demonstrations)
- The proper use of CFD and the equations used
- Finite difference, finite volume, finite element approaches
- Difference scheme and molecules;
- Stability
- Dispersion and Diffusion errors, Cell Re.
- Boundary conditions
Introduction to Advanced Concepts (6L)
- Advanced numerical techniques
- Turbulence modelling
- Mesh generation
- Advanced simulation
- Aerospace CFD in industry lecture
- Pre and post processing
Coursework
Progress Check/Brief Report/Week 6 of Michaelmas term/25%
Coursework/Report/1 Week after end of Michaelmas term/75%
Mesh Generation and Preprocessing (Coursework: approx 2 hours)
- Conversion to Fortran; examples of Fortran programs
- Mesh generation for simplified geometries (eg bend, nozzle, hump, airfoil)
- Preprocessing
2-D Euler, Time Marching CFD Program
(Coursework: 5 mini-exercises of about 2-4 hours each, forming a 16 hour mini-project)
- Finite volume discretisation, evaluation of fluxes. (4h)
- Application of boundary conditions. (2h)
- Time Iteration, simple LAX method. (2h)
- Convergence & accuracy testing. (4h)
- Enhancements, e.g. deferred corrections, Adams - Bashforth RK integration, use of energy equation. (4h)
- Exploration of post-processing
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 title / Interim] Coursework 1 brief description Learning objective: |
Individual Report anonymously marked |
day during term, ex: Thu week 6 [15/60] |
|
[Coursework activity #2 title / Final] Coursework 2 brief description Learning objective: |
Individual Report anonymously marked |
Fri week 10 [45/60] |
Booklists
Please see the Booklist for Group A Courses for references for this module.
Main course text is:
Tucker P. G. 2016. Advanced computational fluid and aerodynamics, Cambridge University Press, ISBN: 9781107428836.
Also, useful advanced material can be found in this text.
Tucker P. G. 2013. Unsteady computational fluid dynamics in aeronautics, Springer, ISBN 978-94-007-7048-5.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 01/06/2018 11:37
Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2023-24
Module Leader
Lab Leader
Timing and Structure
Michaelmas term. In-person lectures and demonstrations. Coursework with integrated lectures. Assessment: 100% coursework.
Prerequisites
3A1 and 3A3 assumed. Pre-module reading about Fortran helpful
Aims
The aims of the course are to:
- provide an introduction to the field of computational fluid mechanics.
- develop an understanding of how numerical techniques are devised.
- implement these techniques in practical computer codes.
- overview the nature of simulation in the future and advanced methods.
Objectives
As specific objectives, by the end of the course students should be able to:
- formulate numerical approximations to partial differential equations.
- write computer programs for solving the resulting difference equations and processing their solutions.
- learn about modern methods to improve simulation accuracy.
- appreciate the capabilities of numerical methods to predict complex flows.
Content
This is a coursework based project. The students write a Computational Fluid Dynamics (CFD) program to solve the Euler equations in 2D with time marching. There are also some basic mesh generation, pre-processing and post-processing tasks. The assessment is through two reports: The first report demonstrates the performance of a basic CFD program and studies basic properties of finite differencing methods. This is to be submitted in Week 6 of the Michaelmas term. The 2nd report demonstrates the coding and performance of more advanced CFD algorithms with discussion on a selected advanced CFD topic. The performance and traits of the extended CFD code are contrasted with expected traits for a range of subsonic, transonic and supersonic flows. The final report is submitted after the end of the Michaelmas term in Week 10.
Writing a CFD Solver and Numerical Concepts (5L)
- The proper use of CFD and the equations used for compressible flows
- Finite difference, finite volume, finite element approaches
- Program specification and structure
- Difference schemes, stability, dispersion and diffusion errors
- Turbulence modelling, adaptive methods, multi-phase flows and parallel computing
- Hyperbolicity and the upwinding method for advection
- Total variation diminishing (TVD) methods
Coursework
Progress Check / Brief Report / Week 6 of Michaelmas term [25%]
Coursework / Report / Week 10 after end of Michaelmas term [75%]
Mesh Generation and Pre-processing (Coursework: approx 2 hours)
- Examples of basic Fortran programs
- Mesh generation for simplified geometries
- Constructing an initial flowfield guess
2-D Euler, Time Marching CFD Program (Coursework: 6 mini-exercises, approx 20 hour project)
- Finite volume discretisation, evaluation of fluxes (4h)
- Application of boundary conditions (2h)
- Time marching, simple LAX method (2h)
- Convergence & accuracy testing (2h)
- Solver enhancements to investigate a choice of challenging test cases (6h)
- Post-processing to produce final report data (4h)
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 / Interim] Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
Thu week 6 [25%] |
|
[Coursework activity #2 / Final] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
Fri week 10 [75%] |
Booklists
Main course text is:
LeVeque R. J. 2002. Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.
Also, useful material can be found in these texts:
Ferziger J. H. and Peric M. 2002. Computational Methods for Fluid Dynamics, Springer.
Toro E. F. 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer
Hirsch C. 1988-1990 Numerical Computation of Internal and External Flows, Volumes 1 and 2, Wiley
Davies R., Rea A. and Tsaptsinos D. Introduction to FORTRAN 90, Student Notes, Queen's University, Belfast
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
Knowledge and Understanding
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 29/09/2023 08:20
Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2017-18
Module Leader
Lecturer
Lab Leader
Timing and Structure
Michaelmas term. Coursework with integrated lectures. Assessment: 100% coursework.
Prerequisites
3A1 and 3A3 assumed. Pre-module reading about Fortran helpful
Aims
The aims of the course are to:
- provide an introduction to the field of computational fluid mechanics.
- help students develop an understanding of how numerical techniques are devised and analysed with solution of fluid flow problems as the target.
- provide some experience in the software engineering skills associated with the implementation of these techniques in practical computer codes.
- illuminate some of the difficulties encountered in the numerical solution of fluid flow problems.
- Overview the nature of simulation in the future and advanced methods relating to this
Objectives
As specific objectives, by the end of the course students should be able to:
- formulate numerical approximations to partial differential equations.
- write computer programs for solving the resulting difference equations.
- understand the limitations of numerical methods and the compromises between accuracy and mean time.
- appreciate the power of numerical solutions to predict complex flows, including shock waves.
- develop the critical skills necessary to respond to and audit simulations produced by CFD for complex flow problems.
Content
This is a course work based project. The students have to write a Computational Fluid Dynamics (CFD) program - in Euler mode with time marching. There is also some basic mesh generation, preprocessing and post processing tasks. The assessment is through two reports. The first report demonstrates the performance of a basic CFD program and some discussion on general aspects of CFD. This needs to be handed in week 6 of the Michaelmas term. The 2nd report demonstrates the coding and performance of more advanced CFD algorithms with discussion on a selected advanced CFD topic. The performance and traits of the extended CFD code are contrasted with expected traits for a range of subsonic and transonic flows. The final report is handed in at the end of the Michaelmas term. The course also allows for some creativity through the design of novel algorithmic approaches.
Introduction and Basic Numerical Concepts (2L including examples, plus demonstrations)
- The proper use of CFD and the equations used
- Finite difference, finite volume, finite element approaches
- Difference scheme and molecules;
- Stability
- Dispersion and Diffusion errors, Cell Re.
- Boundary conditions
Introduction to Advanced Concepts (6L) (Prof. P.G. Tucker)
- Advanced numerical techniques
- Turbulence modelling
- Mesh generation
- Advanced simulation
- Aerospace CFD in industry lecture
- Pre and post processing
Coursework
Progress Check/Brief Report/Week 6 of Michaelmas term/25%
Coursework/Report/End of Michaelmas term/75%
Mesh Generation and Preprocessing (Coursework: approx 2 hours)
- Conversion to Fortran; examples of Fortran programs
- Mesh generation for simplified geometries (eg bend, nozzle, hump, airfoil)
- Preprocessing
2-D Euler, Time Marching CFD Program
(Coursework: 5 mini-exercises of about 2-4 hours each, forming a 16 hour mini-project)
- Finite volume discretisation, evaluation of fluxes. (4h)
- Application of boundary conditions. (2h)
- Time Iteration, simple LAX method. (2h)
- Convergence & accuracy testing. (4h)
- Enhancements, e.g. deferred corrections, Adams - Bashforth RK integration, use of energy equation. (4h)
- Exploration of post-processing
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 title / Interim] Coursework 1 brief description Learning objective: |
Individual/group Report / Presentation [non] anonymously marked |
day during term, ex: Thu week 3 [xx/60] |
|
[Coursework activity #2 title / Final] Coursework 2 brief description Learning objective: |
Individual Report anonymously marked |
Wed week 9 [xx/60] |
Booklists
Please see the Booklist for Group A Courses for references for this module.
Main course text is:
Tucker P. G. 2016. Advanced computational fluid and aerodynamics, Cambridge University Press, ISBN: 9781107428836.
Also, useful advanced material can be found in this text.
Tucker P. G. 2013. Unsteady computational fluid dynamics in aeronautics, Springer, ISBN 978-94-007-7048-5.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 13/10/2017 12:10
Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2021-22
Module Leader
Lecturer
Dr J Li
Lab Leader
Dr J Li
Timing and Structure
Michaelmas term. In-person/online lectures and online demonstrations. Coursework with integrated lectures. Assessment: 100% coursework.
Prerequisites
3A1 and 3A3 assumed. Pre-module reading about Fortran helpful
Aims
The aims of the course are to:
- provide an introduction to the field of computational fluid mechanics.
- help students develop an understanding of how numerical techniques are devised.
- implement these techniques in practical computer codes.
- overview the nature of simulation in the future and advanced methods.
Objectives
As specific objectives, by the end of the course students should be able to:
- formulate numerical approximations to partial differential equations.
- write computer programs for solving the resulting difference equations.
- learn modern TVD shock-capturing methods.
- appreciate the power of numerical solutions to predict complex flows, including shock waves.
Content
This is a course work based project. The students have to write a Computational Fluid Dynamics (CFD) program - in Euler mode with time marching. There is also some basic mesh generation, preprocessing and post processing tasks. The assessment is through two reports. The first report demonstrates the performance of a basic CFD program and studies basic properties of finite difference methods. This needs to be handed in week 6 of the Michaelmas term. The 2nd report demonstrates the coding and performance of more advanced CFD algorithms with discussion on a selected advanced CFD topic. The performance and traits of the extended CFD code are contrasted with expected traits for a range of subsonic and transonic flows. The final report is handed in at the end of the Michaelmas term.
Introduction and Basic Numerical Concepts (2L)
- The proper use of CFD and the equations used
- Finite difference, finite volume, finite element approaches
- Difference scheme and molecules
- Stability, Dispersion and Diffusion errors, Cell Re
- Compressible Flows vs Incompressible Flows
- Single Phase Flows vs Multiphase Flows
- Turbulence Modelling, Adaptive Methods and Parallel Computing
Modern Shock-Capturing Methods for Time-Dependent Compressible Flows (6L)
- Euler Equations and Hyperbolicity
- The Upwinding Method for Advection
- Godunov's Method for Linear System
- Total Variation Diminishing (TVD) Methods
- High-Resolution Methods and Limiters
- Approximate Riemann Solvers
- Roe Solver for Euler Equations
Coursework
Progress Check/Brief Report/Week 6 of Michaelmas term [25%]
Coursework/Report/1 Week after end of Michaelmas term [75%]
Mesh Generation and Preprocessing (Coursework: approx 2 hours)
- Conversion to Fortran; examples of Fortran programs
- Mesh generation for simplified geometries (eg bend, nozzle, hump, airfoil)
- Preprocessing
2-D Euler, Time Marching CFD Program
(Coursework: 5 mini-exercises of about 2-4 hours each, forming a 16 hour mini-project)
- Finite volume discretisation, evaluation of fluxes. (4h)
- Application of boundary conditions. (2h)
- Time Iteration, simple LAX method. (2h)
- Convergence & accuracy testing. (4h)
- Enhancements, e.g. deferred corrections, Adams - Bashforth RK integration, use of energy equation. (4h)
- Exploration of post-processing
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 title / Interim] Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
day during term, ex: Thu week 6 [25%] |
|
[Coursework activity #2 title / Final] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
Fri week 10 [75%] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Main course text is:
LeVeque R. J. 2002. Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.
Also, useful material can be found in these texts.
Ferziger J. H. and Peric M. 2002. Computational Methods for Fluid Dynamics, Springer.
Toro E. F. 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer
Hirsch C. 1988-1990 Numerical Computation of Internal and External Flows, Volumes 1 and 2, Wiley
Davies R., Rea A. and Tsaptsinos D. Introduction to FORTRAN 90, Student Notes, Queen's University, Belfast
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 27/09/2021 13:28
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2021-22
Module Leader
Lecturers
Prof M Girolami, Dr A Kabla and Prof M Gales
Lab Leader
Prof M Girolami
Timing and Structure
Lent term. 16 lectures and coursework.
Aims
The aims of the course are to:
- Teach some mathematical techniques that have wide applicability to many areas of engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
- Calculate the least squares solution of a set of linear equations.
- Understand how to apply Principal Component Analysis (PCA) to a problem.
- Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
- Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
- Understand the definitions and application areas of Stochastic Processes.
- Understand the principle of Markov Chains.
- Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
- Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
- Understand the algorithms of the different gradient search methods.
- Solve unconstrained problems using appropriate search methods.
- Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
- Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.
Content
Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering. Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.
Linear Algebra (4L, Prof G Wells)
- Revision of IB material
- Matrix norms, condition numbers, conditions for convergence of iterative schemes
- Positive definite matrices
- Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
- Principal Component Analysis
- Markov matrices and applications
Stochastic Processes (5L, Prof S Godsill)
- Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
- The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
- Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.
Optimization (7L, Prof M Girolami)
- Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
- Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
- Linear programming (Simplex Method)
- Constrained Optimization: Lagrange and Karush-Kuhn-Tucker (KKT) multipliers; penalty and barrier functions
- Global optimisation: Simulated Annealing
Coursework
Exploring Principal Component Analysis for dimensional reduction and data representation.
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 20/05/2021 07:40
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2023-24
Module Leader
Lecturers
Prof M Girolami, Prof G Wells and Prof M Gales
Lab Leader
Prof M Girolami
Timing and Structure
Lent term. 16 lectures and coursework.
Aims
The aims of the course are to:
- Teach some mathematical techniques that have wide applicability to many areas of engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
- Calculate the least squares solution of a set of linear equations.
- Understand how to apply Principal Component Analysis (PCA) to a problem.
- Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
- Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
- Understand the definitions and application areas of Stochastic Processes.
- Understand the principle of Markov Chains.
- Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
- Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
- Understand the algorithms of the different gradient search methods.
- Solve unconstrained problems using appropriate search methods.
- Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
- Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.
Content
Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering. Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.
Linear Algebra (5L, Prof G Wells)
- Revision of IB material
- Matrix norms, condition numbers, conditions for convergence of iterative schemes
- Positive definite matrices
- Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
- Principal Component Analysis
- Markov matrices and applications
Stochastic Processes (5L, Prof M Gales)
- Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
- The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
- Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.
Optimization (6L, Prof M Girolami)
- Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
- Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
- Linear programming (Simplex Method)
- Constrained Optimization: Lagrange and Karush-Kuhn-Tucker (KKT) multipliers; penalty and barrier functions
Coursework
Exploring Principal Component Analysis for dimensional reduction and data representation.
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 31/12/2023 12:49
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2018-19
Module Leader
Lecturers
Prof G Csanyi, Prof G Wells and Prof M Gales
Lab Leader
Prof G Csanyi
Timing and Structure
Lent term. 16 lectures and coursework.
Aims
The aims of the course are to:
- Teach some mathematical techniques that have wide applicability to many areas of engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
- Calculate the least squares solution of a set of linear equations.
- Understand how to apply Principal Component Analysis (PCA) to a problem.
- Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
- Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
- Understand the definitions and application areas of Stochastic Processes.
- Understand the principle of Markov Chains.
- Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
- Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
- Understand the algorithms of the different gradient search methods.
- Solve unconstrained problems using appropriate search methods.
- Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
- Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.
Content
Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering. Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.
Linear Algebra (4L, Prof G Wells)
- Revision of IB material
- Matrix norms, condition numbers, conditions for convergence of iterative schemes
- Positive definite matrices
- Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
- Principal Component Analysis
- Markov matrices and applications
Stochastic Processes (5L, Prof M Gales)
- Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
- The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
- Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.
Optimization (7L, Prof G Csanyi)
- Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
- Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
- Linear programming (Simplex Method)
- Constrained Optimization: Lagrange and Kuhn-Tucker multipliers; penalty and barrier functions
- Global optimisation: Simulated Annealing
Coursework
Exploring Principal Component Analysis for dimensional reduction and data representation.
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 16/10/2018 16:48
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2022-23
Module Leader
Lecturers
Prof M Girolami and Prof M Gales
Lab Leader
Prof M Girolami
Timing and Structure
Lent term. 16 lectures and coursework.
Aims
The aims of the course are to:
- Teach some mathematical techniques that have wide applicability to many areas of engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
- Calculate the least squares solution of a set of linear equations.
- Understand how to apply Principal Component Analysis (PCA) to a problem.
- Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
- Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
- Understand the definitions and application areas of Stochastic Processes.
- Understand the principle of Markov Chains.
- Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
- Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
- Understand the algorithms of the different gradient search methods.
- Solve unconstrained problems using appropriate search methods.
- Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
- Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.
Content
Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering. Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.
Linear Algebra (4L, Prof G Wells)
- Revision of IB material
- Matrix norms, condition numbers, conditions for convergence of iterative schemes
- Positive definite matrices
- Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
- Principal Component Analysis
- Markov matrices and applications
Stochastic Processes (5L, Prof S Godsill)
- Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
- The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
- Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.
Optimization (7L, Prof M Girolami)
- Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
- Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
- Linear programming (Simplex Method)
- Constrained Optimization: Lagrange and Karush-Kuhn-Tucker (KKT) multipliers; penalty and barrier functions
- Global optimisation: Simulated Annealing
Coursework
Exploring Principal Component Analysis for dimensional reduction and data representation.
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 24/05/2022 12:53
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