High-order wave propagation algorithms for hyperbolic systems.

*(English)*Zbl 1264.65151Summary: We present a finite volume method that is applicable to hyperbolic partial differential equations including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory (WENO) reconstruction in space and strong stability preserving Runge-Kutta integration in time. 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 wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.

Reviewer: Reviewer (Berlin)

##### MSC:

65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |

35L65 | Hyperbolic conservation laws |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |