Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

doi:10.1007/s42967-021-00165-y

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (2): 923-945.doi: 10.1007/s42967-021-00165-y

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Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

Jean-Luc Guermond¹, Bojan Popov¹, Laura Saavedra²

1 Department of Mathematics, Texas A&M University, College Station, USA;
2 Departamento de Matemática Aplicada a la Ingeniería Aeroespacial, Universidad Politécnica de Madrid, Madrid, Spain

收稿日期:2020-12-03 修回日期:2021-08-20 出版日期:2023-06-20 发布日期:2023-05-26
通讯作者: Laura Saavedra, laura.saavedra@upm.es;Jean-Luc Guermond, guermond@math.tamu.edu;Bojan Popov, popov@math.tamu.edu E-mail:laura.saavedra@upm.es;guermond@math.tamu.edu;popov@math.tamu.edu
基金资助:
This material is based upon work supported in part by a "Computational R&D in Support of Stockpile Stewardship" Grant from Lawrence Livermore National Laboratory, the National Science Foundation Grants DMS-1619892, by the Air Force Office of Scientific Research, USAF, under Grant/contract number FA99550-12-0358, and by the Army Research Office under Grant/contract number W911NF-15-1-0517 and by the Spanish MCINN under Project PGC2018-097565-B-I00.

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

Jean-Luc Guermond¹, Bojan Popov¹, Laura Saavedra²

1 Department of Mathematics, Texas A&M University, College Station, USA;
2 Departamento de Matemática Aplicada a la Ingeniería Aeroespacial, Universidad Politécnica de Madrid, Madrid, Spain

Received:2020-12-03 Revised:2021-08-20 Online:2023-06-20 Published:2023-05-26
Contact: Laura Saavedra, laura.saavedra@upm.es;Jean-Luc Guermond, guermond@math.tamu.edu;Bojan Popov, popov@math.tamu.edu E-mail:laura.saavedra@upm.es;guermond@math.tamu.edu;popov@math.tamu.edu
Supported by:
This material is based upon work supported in part by a "Computational R&D in Support of Stockpile Stewardship" Grant from Lawrence Livermore National Laboratory, the National Science Foundation Grants DMS-1619892, by the Air Force Office of Scientific Research, USAF, under Grant/contract number FA99550-12-0358, and by the Army Research Office under Grant/contract number W911NF-15-1-0517 and by the Spanish MCINN under Project PGC2018-097565-B-I00.

摘要/Abstract

摘要： An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving nonlinear 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.

关键词: Conservation equations, Hyperbolic systems, Arbitrary Lagrangian-Eulerian, Moving meshes, Invariant domains, High-order method, Convex limiting, Finite element method

Abstract: An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving nonlinear 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.

Key words: Conservation equations, Hyperbolic systems, Arbitrary Lagrangian-Eulerian, Moving meshes, Invariant domains, High-order method, Convex limiting, Finite element method

中图分类号:

Jean-Luc Guermond, Bojan Popov, Laura Saavedra. Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations[J]. Communications on Applied Mathematics and Computation, 2023, 5(2): 923-945.

参考文献

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Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

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