Extended finite element method in mixed-hybrid model of singular groundwater flow

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24220%2F21%3A00008482" target="_blank" >RIV/46747885:24220/21:00008482 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.matcom.2020.12.018" target="_blank" >https://doi.org/10.1016/j.matcom.2020.12.018</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.matcom.2020.12.018" target="_blank" >10.1016/j.matcom.2020.12.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Extended finite element method in mixed-hybrid model of singular groundwater flow

Popis výsledku v původním jazyce

A model of groundwater flow in porous media influenced by wells (boreholes, channels) is considered. The model is motivated by the reduced dimension approach which suits fractured porous media problems, especially in granite rocks. The wells are modeled as lower dimensional 1d objects intersecting the surrounding bulk rock domain and causing singularities in the solution. The domains are discretized independently resulting in a mesh of mixed dimensions. The extended finite element methods (XFEM) with a proper enrichment is applied to couple the flow between the wells and the bulk rock and to better approximate the singularities. In this contribution, we derive and solve a mixed model for pressure and velocity. We suggest a new enrichment (similar to Stable generalized FEM) for velocity on top of standard zero order Raviart–Thomas finite elements. The properties of the suggested XFEM are validated on a set of numerical tests and the optimal convergence rate is demonstrated. Test cases both in 2d and 3d are presented.

Název v anglickém jazyce

Extended finite element method in mixed-hybrid model of singular groundwater flow

Popis výsledku anglicky

A model of groundwater flow in porous media influenced by wells (boreholes, channels) is considered. The model is motivated by the reduced dimension approach which suits fractured porous media problems, especially in granite rocks. The wells are modeled as lower dimensional 1d objects intersecting the surrounding bulk rock domain and causing singularities in the solution. The domains are discretized independently resulting in a mesh of mixed dimensions. The extended finite element methods (XFEM) with a proper enrichment is applied to couple the flow between the wells and the bulk rock and to better approximate the singularities. In this contribution, we derive and solve a mixed model for pressure and velocity. We suggest a new enrichment (similar to Stable generalized FEM) for velocity on top of standard zero order Raviart–Thomas finite elements. The properties of the suggested XFEM are validated on a set of numerical tests and the optimal convergence rate is demonstrated. Test cases both in 2d and 3d are presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Mathematics and Computers in Simulation

ISSN

0378-4754

e-ISSN

—

Svazek periodika

189

Číslo periodika v rámci svazku

SI

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

30

Strana od-do

207-236

Kód UT WoS článku

000683684700016

EID výsledku v databázi Scopus

2-s2.0-85099587968