An adaptive spectral element method for systems of conservation laws

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509633" target="_blank" >RIV/00216208:11320/25:10509633 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pHLDVXfBRL" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pHLDVXfBRL</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcp.2025.114322" target="_blank" >10.1016/j.jcp.2025.114322</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An adaptive spectral element method for systems of conservation laws

Popis výsledku v původním jazyce

We present a novel method for the numerical solution of systems of conservation laws. For the space discretization, the scheme considers high-order continuous finite elements stabilized via subgrid modeling, as well as highly anisotropic adaptive meshes in order to capture efficiently any sharp features in the solution. Time integration is carried out via a time-step adaptive, linearly implicit Runge-Kutta method, which allows large time steps and requires only the solution of a linear system of equations at each internal stage. An important characteristic of the present method is that the mesh is adapted before solving for the next time interval, and not afterwards as in the common procedure. Furthermore, the error arising from the inexact solution of the linear systems is also estimated and controlled, in such a way that the numerical solution is sufficiently accurate and the linear systems are not oversolved. Numerical experiments, including a computationally difficult case of non-convex flux and the Euler equations for compressible flows, were performed with up to eight-degree elements and a third-order time marching formula to demonstrate the capabilities of the method.

Název v anglickém jazyce

An adaptive spectral element method for systems of conservation laws

Popis výsledku anglicky

We present a novel method for the numerical solution of systems of conservation laws. For the space discretization, the scheme considers high-order continuous finite elements stabilized via subgrid modeling, as well as highly anisotropic adaptive meshes in order to capture efficiently any sharp features in the solution. Time integration is carried out via a time-step adaptive, linearly implicit Runge-Kutta method, which allows large time steps and requires only the solution of a linear system of equations at each internal stage. An important characteristic of the present method is that the mesh is adapted before solving for the next time interval, and not afterwards as in the common procedure. Furthermore, the error arising from the inexact solution of the linear systems is also estimated and controlled, in such a way that the numerical solution is sufficiently accurate and the linear systems are not oversolved. Numerical experiments, including a computationally difficult case of non-convex flux and the Euler equations for compressible flows, were performed with up to eight-degree elements and a third-order time marching formula to demonstrate the capabilities of the method.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Computational Physics

ISSN

0021-9991

e-ISSN

1090-2716

Svazek periodika

541

Číslo periodika v rámci svazku

neuveden

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

38

Strana od-do

114322

Kód UT WoS článku

001566678400002

EID výsledku v databázi Scopus

2-s2.0-105014811308