Genuinely multi-dimensional equilibria preservation on curved domains with a ghost point method for acoustic equations
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In this work we present a novel stationarity preserving numerical method for the solution of hyperbolic problems, with a focus on the linear hyperbolic acoustic system. The method combines multi-dimensional globalization of the fluxes (GF) on Cartesian grids with the ghost point method (GPM) to handle curved domains. The main feature of the method is the embed discrete stationary solutions with zero velocity divergence, which are not preserved by classical methods. The features of the new method are shown on some classical examples, and compared to a standard Rusanov-GPM method that does not preserve the stationary solutions.