Entropy bounded compact stencil Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kumar, Deepak, Rai, Pratima, Patel, Arvind
Institution: University of Delhi
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223378362