Method of Finite Volumes

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The subject is devoted to the numerical solutions of linear partial differential equations of first and second order using the finite difference and the finite volume methods. The lecture discusses the basic properties of numerical methods for solving elliptic, parabolic and hyperbolic equations, the modified equation and the numerical viscosity.

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:

Finite difference method (FDM) for linear conservation law equation (explicit, implicit, upwind). Spectral criterion, CFL condition, stability of numerical schemes. Finite volume method (FVM) for non-linear conservation law equation (Lax-Wendroff, Lax-Friedrichs, Runge-Kutta, predictor-corrector, MacCormack). FVM for multidimensional conservation law equations (extension of the given numerical schemes to FVM - triangles, quadrilaterals). Compositional schemes, FVM for Navier-Stokes equations for compressible and incompressible fluids (artificial viscosity method). Discussion and presentation of problems solved by students in research projects.

Syllabus of tutorials:

Study Objective:

Finite difference and finite volume methods and their application to elliptic, parabolic and hyperbolic equations.

Skills:

Application of FVM to solve the Navier-Stokes equations.

Study materials:

Key references:

[1] Blazek, J.: Computational Fluid Dynamics: Principles and Applications, 2005, Elsevier.

[2] Ferziger, J. H., Peric M.: Computational methods for fluid dynamics, 1996, Springer.

[3] J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer Science & Business Media, 2013

Recommended references:

[4] M. Feistauer: Mathematical Method in Fluid Dynamics, Longman, 1993

[5] Chung, T.J.: Computational Fluid Dynamics, 2002, Cambridge University Press

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: