Undergraduate Teaching 2024-25

Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2023-24

Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2023-24

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Module Leader

Dr J Taylor

Lab Leader

Dr J Taylor

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)

  1. Finite volume discretisation, evaluation of fluxes (4h)
  2. Application of boundary conditions (2h)
  3. Time marching, simple LAX method (2h)
  4. Convergence & accuracy testing (2h)
  5. Solver enhancements to investigate a choice of challenging test cases (6h)
  6. Post-processing to produce final report data (4h)

 

Coursework Format

Due date

& marks

[Coursework activity #1 / Interim]

Coursework 1 brief description

Learning objective:

  • Study basic properties of finite differencing methods
  • Learn to use Linux system and Fortran
  • Complete and validate a basic Euler solver

Individual Report

anonymously marked

Thu week 6

[25%]

[Coursework activity #2 / Final]

Coursework 2 brief description

Learning objective:

  • Extend and improve the Euler solver
  • Use it to investigate challenging flows
  • Understand requirements of CFD in practical use

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.

 
Last modified: 29/09/2023 08:20

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