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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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This content will become publicly available on June 1, 2026
Invariant-domain preserving and locally mass conservative approximation of the Lagrangian hydrodynamics equations
In this paper we construct an explicit approximation for the Lagrangian hydrodynamics equations equipped with an arbitrary equation of state. The approximation of the state variable is done with piecewise constant finite elements and the approximation of the mesh motion is done with higher-order continuous finite elements. The method is invariant-domain preserving and locally mass conservative. The purpose of this method is to be used in combination with higher-order methods to make them invariant domain preserving as well.
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- Award ID(s):
- 2110868
- PAR ID:
- 10640467
- Publisher / Repository:
- Computer Methods in Applied Mechanics and Engineering
- Date Published:
- Journal Name:
- Computer methods in applied mechanics and engineering
- ISSN:
- 0045-7825
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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