Numerical Methods in Fluid Dynamics

The course is not on the list Without time-table

Code	Completion	Credits	Range
01NMDT	ZK	2	2P+0C

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course is focused on the design and properties of numerical methods for solving fluid flow equations. Focus is put

mainly on the finite volume method whose classical and advanced schemes are derived. Selected schemes are analyzed

in terms of stability. The second part is devoted to advanced numerical schemes used in practice. The matter is

concluded by a brief summary of alternative numerical approaches for fluid flow simulation and by a demonstration of

visualization techniques for simulation results.

Requirements:

Syllabus of lectures:

1. Conservation laws in vector form, reference scalar equations (transport equation, wave equation).

2. Classification of linear partial differential equations, method of characteristics. Domain of dependence and domain

of influence.

3. Classical schemes of the finite difference method and the finite volume method in 1D (Lax-Friedrichs scheme,

upwind scheme etc.)

4. Numerical viscosity and dispersion, modified equation.

5. Stability and convergence, spectral stability condition, CFL condition.

6. Unstructured meshes of the finite volume method in 2D and 3D. Numerical schemes in multiple dimensions.

7. Advanced numerical schemes: positive and TVD schemes, MUSCL and PISO schemes,. Higher order schemes

(ENO, WENO), flux limiters.

8. Iterative methods for implicit schemes and their preconditioning, multi-step methods, multigrid methods.

9. A brief survey of other numerical methods in computational fluid dynamics (meshless methods, particle methods,

lattice Boltzmann method)

10. Visualization in computational fluid dynamics.

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] J. Blazek, Computational Fluid Dynamics: Principles and Applications (3rd ed.), Elsevier, 2015.

[2] C. Pozridikis, Computational Fluid Dynamics: Theory, Computation, and Numerical Simulation (2nd ed.), Springer

Science + Business Media LLC, 2017.

[3] J. Tu, Jiyuan, G-H. Yeoh, and C. Liu. Computational Fluid Dynamics: A Practical Approach. Butterworth-

Heinemann, 2018.

Recommended references:

[4] C. Hirsch, Numerical Computation of Internal and External Flows, Volume 1: Fundamentals of Computational

Fluid Dynamics (2nd ed.), Elsevier, 2007.

[5] J. F. Wendt (ed.), Computational Fluid Dynamics: An Introduction, Springer, 2009.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: