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

W01TZ006  ZK  65P  Czech 
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 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 NavierStokes 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.
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 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:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: