High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting

2023/06/22 by Yimin Lin, Jesse Chan, Lin, Yimin +1 · 4 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2306.12663

openalex publication_date 2023/06/22 · openalex created_date 2023/06/24 · openalex updated_date 2026/07/28

Abstract

Subcell limiting strategies for discontinuous Galerkin spectral element methods do not provably satisfy a semi-discrete cell entropy inequality. In this work, we introduce an extension to the subcell and monolithic convex limiting strategies that satisfies the semi-discrete cell entropy inequality by formulating the limiting factors as solutions to an optimization problem. The optimization problem is efficiently solved using a deterministic greedy algorithm. We also discuss the extension of the proposed subcell limiting strategy to preserve general convex constraints. Numerical experiments confirm that the proposed limiting strategy preserves high-order accuracy for smooth solutions and satisfies the cell entropy inequality.

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