Efficient Implementation of ADER Schemes for Euler and Magnetohydrodynamical Flows on Structured Meshes - Comparison with Runge-Kutta Methods - Physics > Computational PhysicsReport as inadecuate




Efficient Implementation of ADER Schemes for Euler and Magnetohydrodynamical Flows on Structured Meshes - Comparison with Runge-Kutta Methods - Physics > Computational Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: ADER Arbitrary DERivative in space and time methods for the time-evolutionof hyperbolic conservation laws have recently generated a fair bit of interest.The ADER time update can be carried out in a single step, which is desirable inmany applications. However, prior papers have focused on the theory whiledownplaying implementation details. The purpose of the present paper is to makeADER schemes accessible by providing two useful formulations of the method aswell as their implementation details on three-dimensional structured meshes. Wetherefore provide a detailed formulation of ADER schemes for conservation lawswith non-stiff source terms in nodal as well as modal space along with usefulimplementation-related detail. We also provide details for the efficient use ofADER schemes in obtaining the numerical flux for conservation laws as well aselectric fields for divergence-free magnetohydrodynamics. An efficientWENO-based strategy for obtaining zone-averaged magnetic fields fromface-centered magnetic fields in MHD is also presented.The schemes catalogued here have been implemented in the first author-sRIEMANN code. The speed of ADER schemes is shown to be almost twice as fast asthat of strong stability preserving Runge-Kutta time stepping schemes for allthe orders of accuracy that we tested.



Author: Dinshaw S. Balsara, Chad Meyer, Michael Dumbser, Huijing Du, Zhiliang Xu

Source: https://arxiv.org/







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