Efficient optimization-based invariant-domain-preserving limiters in solving gas dynamics equations

2025/10/24 by Liu, Chen, Milesis, Dionysis, Shu, Chi-Wang +1 · 2 citations
#65K05 #65K10 #65M60 #90C25 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2510.21080

Abstract

We introduce effective splitting methods for implementing optimization-based limiters to enforce the invariant domain in gas dynamics in high order accurate numerical schemes. The key ingredients include an easy and efficient explicit formulation of the projection onto the invariant domain set, and also proper applications of the classical Douglas-Rachford splitting and its more recent extension Davis-Yin splitting. Such an optimization-based approach can be applied to many numerical schemes to construct high order accurate, globally conservative, and invariant-domain-preserving schemes for compressible flow equations. As a demonstration, we apply it to high order discontinuous Galerkin schemes and test it on demanding benchmarks to validate the robustness and performance of both ℓ¹-norm minimization limiter and ℓ²-norm minimization limiter.

Citations

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Cited by

• Nonnegative Low-Rank Matrix Correction under an Orthogonality Constraint in Conservative Vlasov Simulations
• Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws

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