Mathematical Methods in Fluid Dynamics

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course is devoted to mathematical fundamentals of fluid mechanics models, classical and advanced finite difference and finite volume techniques applied to numerical solution of simplified problems as well as multi - dimensional problems of inviscid and viscous flow.

Requirements:

Basic course of Calculus, Linear Algebra and Ordinary Differential Equations (in the extent of the courses 01MA1, 01MAA2-4, 01LA1, 01LAA2, 01NM held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. conservation laws for viscous compressible fluid flow in differential and integral forms - Navier-Stokes equations

2. Simplified models - Euler equations, potential flow, incompressible flow, 1D problem

3. The model scalar equations (transport equation, diffusion, reaction)

4. Finite volume and finite difference schemes for transport equation

5. Stability criterions for linear problems, numerical viscosity and dispersion

6. Upwind schemes and TVD methods

7. High resolution schemes for nonlinear problems with discontinuities - reconstruction, limiter

8. Extension to system of equations, approximation of diffusive term

9. Schemes for multi-dimensional problems on structured as well as unstructured grids

10. some technical applications

Syllabus of tutorials:

1. conservation laws for viscous compressible fluid flow in differential and integral forms - Navier-Stokes equations

2. Simplified models - Euler equations, potential flow, incompressible flow, 1D problem

3. The model scalar equations (transport equation, diffusion, reaction)

4. Finite volume and finite difference schemes for transport equation

5. Stability criterions for linear problems, numerical viscosity and dispersion

6. Upwind schemes and TVD methods

7. High resolution schemes for nonlinear problems with discontinuities - reconstruction, limiter

8. Extension to system of equations, approximation of diffusive term

9. Schemes for multi-dimensional problems on structured as well as unstructured grids

10. some technical applications

Study Objective:

acquaints with models and numerical solutions of nonlinear problems described by the partial differential equations of mostly hyperbolic or parabolic-hyperbolic types and its systems.

Study materials:

Key references:

R.J. LeVeque: Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, ISBN 0 521 81087 6, 2002

Recommended references:

J. Blazek: Computational Fluid Dymanics" Principles and Applications, Elsevier, ISBN 0 08 043009 0, 2001

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: