Entropy bounded compact stencil Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws
Abstract
In this paper we introduce a compact stencil Runge-Kutta discontinuous Galerkin method for the Euler equations of compressible gas dynamics, which preserves a minimum entropy principle similar to that introduced by Tadmor for entropy solution of the Euler equations [4]. Compact stencil RKDG, introduced by Chen et al. in [15], is a variant of standard RKDG method which is known for its smaller stencil size and parallel efficiency. The main challenge is that the cRKDG method has to be expressed in Butcher form and not every Runge-Kutta method of this form is a convex combination of forward-Euler steps. Therefore, in order to establish this property we leverage the bound preserving framework of the cRKDG schemes [8], an entropy bounded limiter [6] and the classical positivity preserving limiter. In the last section numerical experiments are provided to demonstrate the robustness of the method.
Related
- Fully discrete multi-entropy-stable compact Runge--Kutta discontinuous Galerkin methods for hyperbolic conservation laws
- A class of high-order discontinuous-Galerkin methods satisfying infinitely many entropy conditions with provable error estimates and strong convergence for general nonlinear conservation laws
- A merged-cell discontinuous Galerkin method for scalar conservation laws on curved domains
- Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form
- GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms
BibTeX
@misc{kumar2026entropy,
title = {{Entropy bounded compact stencil Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws}},
author = {Deepak Kumar and Pratima Rai and Arvind Patel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30496},
eprint = {2610.30496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30496},
}
RIS
TY - UNPB
TI - Entropy bounded compact stencil Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws
AU - Deepak Kumar
AU - Pratima Rai
AU - Arvind Patel
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30496
UR - https://arxiv.org/abs/2610.30496
AB - In this paper we introduce a compact stencil Runge-Kutta discontinuous Galerkin method for the Euler equations of compressible gas dynamics, which preserves a minimum entropy principle similar to that introduced by Tadmor for entropy solution of the Euler equations [4]. Compact stencil RKDG, introduced by Chen et al. in [15], is a variant of standard RKDG method which is known for its smaller stencil size and parallel efficiency. The main challenge is that the cRKDG method has to be expressed in Butcher form and not every Runge-Kutta method of this form is a convex combination of forward-Euler steps. Therefore, in order to establish this property we leverage the bound preserving framework of the cRKDG schemes [8], an entropy bounded limiter [6] and the classical positivity preserving limiter. In the last section numerical experiments are provided to demonstrate the robustness of the method.
ER -