AI & ML
Entropy bounded compact stencil Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws
arXiv cs.NA0 views
arXiv:2610.30496v1 Announce Type: new 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:https://arxiv.org/abs/2610.30496PreviousDiscovery of Singularities in Partial Differential Equations Using Adaptive Numerical DiscretizationsNextThe reverse Ritz inclusion: computable bounds on the pseudospectra of an operator by those of a finite-rank compression
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