Maths C42H 3042: Computational Methods for Gas Dynamcs
Summary: This course provides an introduction to modern numerical methods for gas dynamics, compressible flows and hyperbolic conservation laws in general. By completion, students will be able to evolve physically interesting models and have confidence in the solution. Emphasis will be on the algorithms used and not on the theory of gas dynamics. Some programming will be required but a minimal background will be assumed.
Syllabus: (detailed) Hyperbolic equations and systems, characteristics, conservation laws, Eulers equations of gas dynamics, entropy solutions, linear numerical methods and their convergence, conservative schemes, nonlinear numerical methods and their convergence, solving Riemann problems, Godunov methods, higher-order methods, shock waves and other applications.
Prerequisites: A basic second year maths methods course such as ENGN2004 or B14. Basic knowledge of eigenproblem and Fourier expansions will be useful. Courses such as B23H, B34H and B21H will be an advantage.
Lectures and Pracs: Lectures are Tuesday 11am and Thursday 11am in Rm 1179 of the John Dedman Bldg. Prac sessions/tutes in LG6 of the Dedman Bldg at 2pm Tuesdays.
Assessment: A combination of assignments and exam to be determined in consultation with enrolled students.
Provided material: Exercise sheet 1 Example code Assignment Corrections to lecture notes, exercises, example code and assignments
Programming: Practical exercises will be carried out in Matlab, Fortran and/or C.
- LeVeque, R.J., Numerical Methods for Conservation Laws, Birkhauser (1988) [Copy in Hancock is on 2 day loan only]
- Colella and Puckett, Modern Numerical Methods for Fluid Flow, course notes [somewhat incomplete]
- Strikwerda, Finite Difference Schemes and Partial Differential Equations [technical analysis of linear schemes]
- Richtmyer and Morton, Difference Methods for Initial Value Problems [classic]
- Roache, Computational Fluid Dynamics [CFD other than this course - a bit dated]