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	Scientific Computing in Partial Differential Equations

2WN13 - Scientific Computing in Partial Differential Equations

Teacher
Dr.Ir. J.H.M. ten Thije Boonkkamp
HG 8.30, tenthije@win.tue.nl
Scientific Computing
Faculty of Mathematics and Computer Science

Short description of objectives and content

The course deals with numerical methods for elliptic, parabolic and hyperbolic PDEs. In particular, questions like accuracy and (in)stability of a numerical scheme, dissipation, dispersion and conservation are studied. These notions are applied to numerical schemes for the Poisson equation, heat equation, wave equation and first order (system of) conservation laws. An important area of application is fluid mechanics. Although some emphasis will be on understanding the phenomenae behind the approximation, a number of practical issues will be discussed as well.

Overview of the material:

Examples of model problems: thermal explosion, heat conduction in a solid, propagation of water waves, shallow water equations.

Elliptic equations: finite difference and finite volume methods, numerical approximation of boundary conditions, error estimates, Stokes equations.

Parabolic equations: finite difference methods, local/global discretisation error, explicit/implicit methods, von Neumann stability analysis, matrix method, Stefan problem.

Hyperbolic equations: characteristics, dispersion relation, nonlinear equations, weak solution, finite difference and finite volume method, stability analysis, numerical dispersion relation, high-resolution schemes, flux limiters, numerical boundary conditions.

Advection-diffusion equations: finite difference methods and finite volume methods; modified equations.

study guide (pdf)

thermexplo-incomplete (m)

initial guess (eps)

final solution (eps)

sphere-incomplete (m)

test (m)

advec1 (m)

advec2 (m)

limiter (m)

traffic-incomplete (m)

swe-incomplete (m)

solveG (m)

g (m)

dg (m)