Webpage for the paper:
High-Order Wave Propagation Algorithms for General Hyperbolic Systems
by D.I. Ketcheson, M. Parsani, and R.J. LeVeque
Submitted to SISC, 2011.
Abstract:
We present a finite volume method that is applicable to general hyperbolic PDEs,
including non-conservative and spatially varying systems. The method can be
extended to arbitrarily high order of accuracy and allows a well-balanced
implementation for capturing solutions of balance laws near steady state. This
well-balancing is achieved through the f-wave Riemann solver and a novel wave-slope
WENO reconstruction procedure. The spatial discretization, like that of the
well-known Clawpack software, is based on solving Riemann problems and calculat-
ing fluctuations (not fluxes). Our implementation employs weighted essentially
non-oscillatory reconstruction in space and strong stability preserving Runge-Kutta
integration in time. We demonstrate the wide applicability and advantageous
properties of the method through numer- ical examples, including problems in
non-conservative form, problems with spatially varying fluxes, and problems
involving near-equilibrium solutions of balance laws.
Preprint of 9 April 2011: pdf file
Source code:
See
https://bitbucket.org/ketch/sharpclaw#sharpClawPaper
To plot results, one also needs
https://bitbucket.org/ketch/clawpack4petclaw#sharpClawPaper