High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting
Numerical Analysis
2023-11-28 v2 Numerical Analysis
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.
Cite
@article{arxiv.2306.12663,
title = {High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting},
author = {Yimin Lin and Jesse Chan},
journal= {arXiv preprint arXiv:2306.12663},
year = {2023}
}