Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489231" target="_blank" >RIV/00216208:11320/24:10489231 - isvavai.cz</a>

Výsledek na webu

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

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcp.2024.113305" target="_blank" >10.1016/j.jcp.2024.113305</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations

Popis výsledku v původním jazyce

We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation using a monolithic convex limiting (MCL) strategy. Failure to discretize the convective derivatives and source terms in a compatible manner produces spurious ripples, e.g., in regions where the coefficients of the continuous problem are constant and the exact solution is linear. We cure this deficiency by incorporating source term components into the fluxes and intermediate states of the MCL procedure. The design of our new limiter is motivated by the desire to preserve simple steady-state equilibria exactly, as in well-balanced schemes for the shallow water equations. The results of our numerical experiments for two-dimensional CDR problems illustrate potential benefits of well-balanced flux limiting in the scalar case.

Název v anglickém jazyce

Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations

Popis výsledku anglicky

We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation using a monolithic convex limiting (MCL) strategy. Failure to discretize the convective derivatives and source terms in a compatible manner produces spurious ripples, e.g., in regions where the coefficients of the continuous problem are constant and the exact solution is linear. We cure this deficiency by incorporating source term components into the fluxes and intermediate states of the MCL procedure. The design of our new limiter is motivated by the desire to preserve simple steady-state equilibria exactly, as in well-balanced schemes for the shallow water equations. The results of our numerical experiments for two-dimensional CDR problems illustrate potential benefits of well-balanced flux limiting in the scalar case.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-01591S" target="_blank" >GA22-01591S: Matematická teorie a numerická analýza rovnic vazkých newtonovských stlačitelných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

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

518

Číslo periodika v rámci svazku

1 December 2024

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

113305

Kód UT WoS článku

001287626900001

EID výsledku v databázi Scopus

2-s2.0-85200158884