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

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