ENGINEERING TRIPOS PART IIB - 2012/2013

Module 4A2 - Computational Fluid Dynamics

AIMS

This module aims 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.

LECTURE SYLLABUS

Basic Numerical Concepts (2L including examples), plus demonstrations)

• Finite difference, finite volume, finite element approaches
• Difference scheme and molecules;
• Stability
• Dispersion and Diffusion errors, Cell Re.
• Boundary conditions

Introduction to Advanced Concepts (4L) (Prof. P.G. Tucker)

• Advanced numerical techniques
• Complex modelling - DNS/LES/RANS
• Complex geometries - Geometry definition, mesh generation, parallel computing
• Aerospace CFD in industry lecture

COURSEWORK

Mesh generation (Coursework: approx 2 hours)

• Conversion to Fortran; examples of Fortran programs
• Mesh generation for simplified geometries (eg bend, nozzle, hump, airfoil)

2-D Euler/Time Matching

(Coursework: 5 mini-exercises of about 2-4 hours each, forming a 16 hour mini-project)

1. Finite volume discretisation, evaluation of fluxes. (4h)
2. Application of boundary conditions. (2h)
3. Time Iteration, simple LAX method. (2h)
4. Convergence & accuracy testing. (4h)
5. Enhancements, e.g. deferred corrections, Adams - Bashforth RK integration, use of energy equation. (4h)

OBJECTIVES

1. To be able to formulate numerical approximations to partial differential equations.
2. To be able to write computer programs for solving the resulting difference equations.
3. To understand the limitations of numerical methods and the compromises between accuracy and mean time.
4. To appreciate the power of numerical solutions to predict complex flows, including shock waves.
5. To develop the critical skills necessary to respond to and audit simulations produced by CFD for complex flow problems.

REFERENCES

Please see the Booklist for Group A Courses for references for this module.

Last updated: September 2012