Tsunami run-up. Courtesy: Hubert Velten of class 06-07:
Impression
This course concerns the numerical discretization of partial differential
equations (PDE's), and the implementation and testing thereof in realistic exercises.
Parabolic and hyperbolic equations encountered in mathematics, physics,
and engineering are discretized with finite difference and finite volume methods.
The focus lies on PDE's with a time and one spatial dimension.
Accuracy and stability of the numerical discretizations are considered in theoretical analysis,
and this analysis is applied in practical exercises from science and engineering.
After successful completion of the course, students are able to start
designing, implementing and testing discretizations of partial differential equations
in their own field.
Three exercises need to be completed with a theoretical part (with set in term deadlines)
and a numerical part (with wider deadlines).
Recent theoretical and numerical exercises concerned recent topics in:
Introduction and classification of PDE's in parabolic, hyperbolic, and elliptic equations.
Parabolic equations:
accuracy and stability of finite difference approximations;
Fourier analysis, explicit method; implicit method, Thomas algorithm, three-level scheme;
more general boundary conditions, conservation; two dimensions, ADI.
Hyperbolic equations: finite difference methods in one dimension,
analytical properties and numerical discretization of conservation laws,
upwind and Lax-Wendroff schemes;
finite volume methods in one dimension, weak formulation, Riemann problem,
conservative methods, Godunov scheme.
Course Material
K.W. Morton and D.F. Mayers,
Numerical Solution of Partial Differential Equations. Cambridge University Press 2005.
Reader: Upwind discretization for conservation laws,Van der Vegt and Bokhove.
See blackboard page.
