Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

Jean-Luc Guermond; Bojan Popov; Laura Saavedra

doi:10.1007/s42967-021-00165-y

Communications on Applied Mathematics and Computation ›› 2021, Vol. 5 ›› Issue (2) : 923-945. DOI: 10.1007/s42967-021-00165-y

Original Paper

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

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Abstract

An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed. The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements. The method is made invariant domain preserving for the Euler equations using convex limiting and is tested on various benchmarks.

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Jean-Luc Guermond, Bojan Popov, Laura Saavedra. Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations. Communications on Applied Mathematics and Computation, 2021, 5(2): 923‒945 https://doi.org/10.1007/s42967-021-00165-y

Funding

Ministerio de Ciencia, Innovación y Universidades(PGC2018-097565-B-I00); Lawrence Livermore National Laboratory(Computational R&D in Support of Stockpile Stewardship); National Science Foundation(DMS-1619892); Air Force Office of Scientific Research(FA99550-12-0358); Army Research Office(W911NF-15-1-0517); Universidad Politécnica de Madrid