ORIGINAL PAPER

Single-Step Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for 1-D Euler Equations

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  • 1 Department of Mathematics, University of Würzburg, Würzburg, Germany;
    2 TIFR Center for Applicable Mathematics, Bangalore, India

Received date: 2019-03-06

  Revised date: 2019-09-17

  Online published: 2020-09-11

Abstract

We propose an explicit, single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations. The grid is moved with the local fuid velocity modifed by some smoothing, which is found to considerably reduce the numerical dissipation introduced by Riemann solvers. The scheme preserves constant states for any mesh motion and we also study its positivity preservation property. Local grid refnement and coarsening are performed to maintain the mesh quality and avoid the appearance of very small or large cells. Second, higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.

Cite this article

Jayesh Badwaik, Praveen Chandrashekar, Christian Klingenberg . Single-Step Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for 1-D Euler Equations[J]. Communications on Applied Mathematics and Computation, 2020 , 2(4) : 541 -579 . DOI: 10.1007/s42967-019-00054-5

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