Numerical Solution of Partial Differential Equations by Finite Difference and Finite Volume Methods

Course guarantor:

Jiří Fürst

Lecturer:

Jaroslav Fořt, Jiří Fürst, Martin Luxa

Tutor:

Jaroslav Fořt, Jiří Fürst, Martin Luxa

Supervisor:

Department of Technical Mathematics

Synopsis:

Aim:

Students are acquainted with mathematical background of two types of numerical methods for partial differential equations (PDR)– finite difference and finite volume methods - and its application.

Basic ideas of finite difference method and principles of its analysis. Implicit and explicit schemes for model PDR of first and second order and its analysis.

Principles of finite volume methods. Mathematical formulation of model PDR, Euler and Navier-Stokes equations as conservation laws. Conservative scheme and numerical flux.

Approximation of convective flux. Riemann problem. Advanced upwind schemes in 1D, extension to high resolution method. Approximation of dissipative flux; temporal discretization.

Link among physical problem, mathematical model, principles of numerical solution and interpretation of numerical simulations in technical applications.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Quarteroni A., Sacco R., Saleri F. : Numerical Mathematics, 2000, Springer.

Blazek, J.: Computational Fluid Dynamics: Principles and Applications, 2001, Elsevier.

Toro, E.F.: Riemann solvers and Numerical Methods for Fluid Dynamics, 1997, Springer.

Le Veque, R.: Finite Volume Methods For Hyperbolic Problems, 2004, Cambridge University Press.

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: