Numerical Solution of Partial Differential Equations by Finite Difference and Finite Volume Methods
Code  Completion  Credits  Range 

W01A007  ZK  60B 
 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 transportdissipation equation (conservation laws). Modified equation and numerical viscosity. Finite volume method in two space variables. Systém of linear PDE, Euler and NavierStokes equations.
 Requirements:
 Syllabus of lectures:

13Approximation, stability, convergence
Analysis of schemes for linear PDE of 1st and 2nd order
Examples of computations
481D nonlinear transport equation, transportdissipation equation.
Basic schemes in forms of finite differences and finite volumes
modern nonlinear schemes of higher order
TVD schemes, reconstruction, limiter.
Examples of computation.
912Linear 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
1314Systems of equations, Euler, NavierStokes equations
Examples of Computations
 Syllabus of tutorials:

13Approximation, stability, convergence
Analysis of schemes for linear PDE of 1st and 2nd order
Examples of computations
481D nonlinear transport equation, transportdissipation equation.
Basic schemes in forms of finite differences and finite volumes
modern nonlinear schemes of higher order
TVD schemes, reconstruction, limiter.
Examples of computation.
912Linear 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
1314Systems of equations, Euler, NavierStokes equations
Examples of Computations
 Study Objective:
 Study materials:

Dvořák, R., Kozel, K.: Matematické modelování v aerodynamice, ČVUT, 1996
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: