Stability and error estimates of a linear numerical scheme approximating nonlinear fluid-structure interactions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10510273" target="_blank" >RIV/00216208:11320/25:10510273 - isvavai.cz</a>

Výsledek na webu

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

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00211-025-01461-y" target="_blank" >10.1007/s00211-025-01461-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Stability and error estimates of a linear numerical scheme approximating nonlinear fluid-structure interactions

Popis výsledku v původním jazyce

In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that works in the reference domain, meaning that no re-meshing is needed during the numerical simulation. For time discretization, we employ the backward Euler method. For space discretization, we respectively use P1-bubble, P1, and P1 finite elements for the approximation of the fluid velocity, pressure, and structure displacement. We show that our method fulfills the geometrical conservation law and dissipates the total energy on the discrete level. Moreover, we prove the (optimal) linear convergence with respect to the sizes of the time step tau and the mesh h. We present numerical experiments involving a substantially deforming fluid domain that do validate our theoretical results. A comparison with a fully implicit (thus nonlinear) scheme indicates that our semi-implicit linear scheme is faster and as accurate as the fully implicit one, at least in stable configurations.

Název v anglickém jazyce

Stability and error estimates of a linear numerical scheme approximating nonlinear fluid-structure interactions

Popis výsledku anglicky

In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that works in the reference domain, meaning that no re-meshing is needed during the numerical simulation. For time discretization, we employ the backward Euler method. For space discretization, we respectively use P1-bubble, P1, and P1 finite elements for the approximation of the fluid velocity, pressure, and structure displacement. We show that our method fulfills the geometrical conservation law and dissipates the total energy on the discrete level. Moreover, we prove the (optimal) linear convergence with respect to the sizes of the time step tau and the mesh h. We present numerical experiments involving a substantially deforming fluid domain that do validate our theoretical results. A comparison with a fully implicit (thus nonlinear) scheme indicates that our semi-implicit linear scheme is faster and as accurate as the fully implicit one, at least in stable configurations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Numerische Mathematik

ISSN

0029-599X

e-ISSN

0945-3245

Svazek periodika

157

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

55

Strana od-do

1023-1077

Kód UT WoS článku

001450748900001

EID výsledku v databázi Scopus

2-s2.0-105000663617