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

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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 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.

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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.

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No time-table has been prepared for this course

The course is a part of the following study plans: