Next: Gas dynamic tests
Abstract:
Global composition of several time steps of the two-step Lax-Wendroff
scheme followed by a Lax-Friedrichs step seems to enhance the best
features of both, although only first order accurate. We show this by
means of some examples of one-dimensional shallow water flow over an
obstacle. In two dimensions we present a new version of Lax-Friedrichs
and an associated second order predictor-corrector method.
Composition of these schemes is shown to be effective and efficient
for some two-dimensional Riemann problems and for Noh's infinite
strength cylindrical shock problem. We also show comparable results
for composition of the predictor-corrector scheme with a modified
second order accurate WENO scheme. That composition is second order
but is more efficient and has better symmetry properties than WENO
alone. For scalar advection in two dimensions the optimal stability of
the new predictor-corrector scheme is shown using computer algebra. We
also show that the generalization of this scheme to three dimensions
is unstable, but using sampling we are able to show that the
composites are sub-optimally stable.
Keywords
composite schemes, conservation laws, hyperbolic systems,
Lax-Wendroff scheme, Lax-Friedrichs scheme, 2D Riemann problem
Full paper (Postscript)
Next: Gas dynamic tests
Richard Liska