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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

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

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Code Completion Credits Range Language
W01TZ006 ZK 65P Czech
Garant předmětu:
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 2023/2024:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
roomKN:D-104
Fořt J.
13:15–16:45
(lecture parallel1)
Karlovo nám.
Konzultační místnost 12101
Wed
Thu
Fri
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-23
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