Richard Liska
Faculty of Nuclear Sciences and Physical Engineering
Czech Technical University in Prague
Czech Republic
liska@siduri.fjfi.cvut.cz
http://www-troja.fjfi.cvut.cz/~liska
Collaborators:
Burton Wendroff, Los Alamos National Laboratory
Stanly Steinberg, University of New Mexico
Hoon Hong, North Carolina State University
Computer algebra can support the development of numerical finite difference codes for solving partial differential equations (PDEs) on several stages of the development process, typically in situations involving processing of large formulas. The stages include transforming and posedness analysis of PDEs, discretization of PDEs into finite difference schemes (FDSs), analysis of the schemes properties like approximation or stability and finaly code generation which automaticaly generate numerical source programs solving given FDS. The experience from several fluid flow models for which the application of symbolic computing proved to be essential during different stages will be presented. The fluid flow models include 1D incompressible and inviscous vertically averaged, hydrostatic shallow water and dispersive Green-Naghdi equations and 2D shallow water equations on plane and on sphere. Shallow water equations are hyperbolic conservation laws for which we have developped centered composite difference schemes based on composing several time steps of oscilatory Lax-Wendroff type scheme with one time step of diffusive Lax-Friedrichs type scheme. For stabilization of the 3D Lax-Wendroff type scheme we have used modified equation approach.