A limiter-based approach to construct high-order fully-discrete entropy stable explicit DG schemes for hyperbolic conservation laws
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912986760740864 |
|---|---|
| author | Liu, Yuchang Guo, Wei Jiang, Yan Sun, Zheng |
| author_facet | Liu, Yuchang Guo, Wei Jiang, Yan Sun, Zheng |
| contents | This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell averages of classical DG solutions with forward Euler time stepping satisfy an ``entropy-stable-like'' property. Building on this result, fully-discrete entropy stability is rigorously enforced through a simple Zhang--Shu-type scaling limiter [45] applied as a post-processing step, without modifying the underlying spatial discretization. Furthermore, the proposed methodology can simultaneously enforce multiple cell entropy inequalities, a capability unavailable in existing ES DG schemes. High-order accuracy in time is achieved by using strong-stability-preserving (SSP) multistep methods. Theoretically, we prove that the proposed scheme indeed maintains high-order accuracy and establish a Lax--Wendroff-type theorem guaranteeing that the limit of the numerical solutions, if it exists, satisfies the desired entropy inequality. Extensive numerical tests for scalar equations and systems, including the nonconvex Buckley--Leverett problem and extreme examples of Euler equations, demonstrate optimal accuracy, enforcement of multiple entropy conditions, and strong robustness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27478 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A limiter-based approach to construct high-order fully-discrete entropy stable explicit DG schemes for hyperbolic conservation laws Liu, Yuchang Guo, Wei Jiang, Yan Sun, Zheng Numerical Analysis This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell averages of classical DG solutions with forward Euler time stepping satisfy an ``entropy-stable-like'' property. Building on this result, fully-discrete entropy stability is rigorously enforced through a simple Zhang--Shu-type scaling limiter [45] applied as a post-processing step, without modifying the underlying spatial discretization. Furthermore, the proposed methodology can simultaneously enforce multiple cell entropy inequalities, a capability unavailable in existing ES DG schemes. High-order accuracy in time is achieved by using strong-stability-preserving (SSP) multistep methods. Theoretically, we prove that the proposed scheme indeed maintains high-order accuracy and establish a Lax--Wendroff-type theorem guaranteeing that the limit of the numerical solutions, if it exists, satisfies the desired entropy inequality. Extensive numerical tests for scalar equations and systems, including the nonconvex Buckley--Leverett problem and extreme examples of Euler equations, demonstrate optimal accuracy, enforcement of multiple entropy conditions, and strong robustness. |
| title | A limiter-based approach to construct high-order fully-discrete entropy stable explicit DG schemes for hyperbolic conservation laws |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.27478 |