Mathematical Methods in Fluid Dynamics
Code  Completion  Credits  Range  Language 

01MMDT2  ZK  2  2+0  Czech 
 Garant předmětu:
 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, 01MAA24, 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  NavierStokes 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 multidimensional 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  NavierStokes 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 multidimensional 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 parabolichyperbolic 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 timetable has been prepared for this course
 The course is a part of the following study plans:

 Matematické inženýrství (elective course)