Efficient, High Accuracy ADER-WENO Schemes for Hydrodynamics and Divergence-Free Magnetohydrodynamics - Physics > Computational PhysicsReport as inadecuate




Efficient, High Accuracy ADER-WENO Schemes for Hydrodynamics and Divergence-Free Magnetohydrodynamics - Physics > Computational Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: The present paper introduces a class of finite volume schemes of increasingorder of accuracy in space and time for hyperbolic systems that are inconservation form. This paper specifically focuses on Euler system that is usedfor modeling the flow of neutral fluids and the divergence-free, idealmagnetohydrodynamics MHD system that is used for large scale modeling ofionized plasmas.Efficient techniques for weighted essentially non-oscillatory WENOinterpolation have been developed for finite volume reconstruction onstructured meshes. We also present a new formulation of the ADER for ArbitraryDerivative Riemann Problem schemes that relies on a local continuousspace-time Galerkin formulation instead of the usual Cauchy-Kovalewskiprocedure.The schemes reported here have all been implemented in the RIEMANN frameworkfor computational astrophysics. We demonstrate that the ADER-WENO meet theirdesign accuracies. Several stringent test problems of Euler flows and MHD flowsare presented in one, two and three dimensions. Many of our test problemsinvolve near infinite shocks in multiple dimensions and the higher orderschemes are shown to perform very robustly and accurately under all conditions.



Author: Dinshaw S. Balsara, Tobias Rumpf, Michael Dumbser, Claus-Dieter Munz

Source: https://arxiv.org/







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