High-Order Wave Propagation Algorithms for General Hyperbolic Systems

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 calculating 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 numerical examples, including problems in non-conservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.