High-order well-balanced finite-volume schemes for barotropic flows: Development and numerical comparisons

High-order well-balanced finite-volume schemes for barotropic flows. Development and numerical comparisons

Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a numerical scheme shall capture such flows efficiently, it should be able to preserve the unperturbed equilibrium state at the discrete level. Here we present a class of schemes of any desired order of accuracy which preserve the lake at rest perfectly. These schemes should have an impact for studying imp...

High-order Well-balanced Schemes

High-order well-balanced finite volume WENO schemes for shallow water equation with moving water

A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Recently a number of so-called well-balanced schemes were developed which satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. In most cases, applications t...

High order well-balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres