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

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

Numerical solution of linear partial diferential equations of first and second order. Properties of numerical methods for elliptic, parabolic and hyperbolic PDE. Finite difference method and finite volume method. Nonlinear transport equation and transport-dissipation equation (conservation laws). Modified equation and numerical viscosity. Finite volume method in two space variables. Systém of linear PDE, Euler and Navier-Stokes equations.

Requirements:

Syllabus of lectures:

1-3Approximation, stability, convergence

Analysis of schemes for linear PDE of 1st and 2nd order

Examples of computations

4-81D nonlinear transport equation, transport-dissipation equation.

Basic schemes in forms of finite differences and finite volumes

modern nonlinear schemes of higher order

TVD schemes, reconstruction, limiter.

Examples of computation.

9-12Linear and nonlinear scalar equation in two space variables,

finite volume method in 2D

Structured, unstructured grid.

Finite volumes of cell centered, cell vertex and dual types

2D schemes

Examples of computations

13-14Systems of equations, Euler, Navier-Stokes equations

Examples of Computations

Syllabus of tutorials:

1-3Approximation, stability, convergence

Analysis of schemes for linear PDE of 1st and 2nd order

Examples of computations

4-81D nonlinear transport equation, transport-dissipation equation.

Basic schemes in forms of finite differences and finite volumes

modern nonlinear schemes of higher order

TVD schemes, reconstruction, limiter.

Examples of computation.

9-12Linear and nonlinear scalar equation in two space variables,

finite volume method in 2D

Structured, unstructured grid.

Finite volumes of cell centered, cell vertex and dual types

2D schemes

Examples of computations

13-14Systems of equations, Euler, Navier-Stokes equations

Examples of Computations

Study Objective:

Study materials:

Dvořák, R., Kozel, K.: Matematické modelování v aerodynamice, ČVUT, 1996

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: