Year: 2026
Type: preprint
Abstract: We introduce the concept of volume term adaptivity for high-order discontinuous Galerkin (DG) schemes solving time-dependent partial differential equations. Termed v-adaptivity, we present a novel general approach that exchanges the discretization of the volume contribution of the DG scheme at every Runge-Kutta stage based on suitable indicators. Depending on whether robustness or efficiency is the main concern, different adaptation strategies can be chosen. Precisely, the weak form volume term discretization is used instead of the entropy-conserving flux-differencing volume integral whenever the former produces more entropy than the latter, resulting in an entropy-stable scheme. Conversely, if increasing the efficiency is the main objective, the weak form volume integral may be employed as long as it does not increase entropy beyond a certain threshold or cause instabilities. Thus, depending on the choice of the indicator, the v-adaptive DG scheme improves robustness, efficiency and approximation quality compared to schemes with a uniform volume term discretization. We thoroughly verify the accuracy, linear stability, and entropy-admissibility of the v-adaptive DG scheme before applying it to various compressible flow problems in two and three dimensions.
Source: arXiv (Cornell University)
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Awards: EsCUT: Entropystabile höhereOrdnung CUTcell discontinuous Galerkin Verfahren, FOR 5409: Strukturerhaltende numerische Methoden für Volumen und Übergangskopplung von heterogenen Modellen, G3044548687, G3403773028, Zugängliches Höchstleistungsrechnen mit Trixi.jl und der Programmiersprache Julia, Modellkaskaden für stochastische TeilchenSimulationen von verdünnten, mehratomigen Gasen
OpenAlex ID: W7141771989
Cites:
Cited by:
Related to: