A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media

被引：41

作者：

Ambartsumyan, Ilona ^{[1
,2
]}

Ervin, Vincent J. ^{[3
]}

Truong Nguyen ^{[2
]}

Yotov, Ivan ^{[2
]}

机构：

[1] Univ Texas Austin, Oden Inst Computat Engn & Sci, Austin, TX 78712 USA

[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[3] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS | 2019年 / 53卷 / 06期

关键词：

Fluid-poroelastic structure interaction; Stokes-Biot model; fractured poroelastic media; non-Newtonian fluid; FLOW; APPROXIMATION; INTERPOLATION; SURFACE;

D O I：

10.1051/m2an/2019061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. We establish existence and uniqueness of a solution to the weak formulation and its semidiscrete continuous-in-time finite element approximation. We present error analysis, complemented by numerical experiments.

引用

页码：1915 / 1955

页数：41

共 47 条

[1]

Acosta G, 2011, MATH COMPUT, V80, P141

[2] A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model [J].

Ambartsumyan, Ilona ;

Khattatov, Eldar ;

Yotov, Ivan ;

Zunino, Paolo .

NUMERISCHE MATHEMATIK, 2018, 140 (02) :513-553

[3] Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction [J].

Badia, Santiago ;

Quaini, Annalisa ;

Quarteroni, Alfio .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (21) :7986-8014

[4] BOUNDARY CONDITIONS AT A NATURALLY PERMEABLE WALL [J].

BEAVERS, GS ;

JOSEPH, DD .

JOURNAL OF FLUID MECHANICS, 1967, 30 :197-&

[5] General theory of three-dimensional consolidation [J].

Biot, MA .

JOURNAL OF APPLIED PHYSICS, 1941, 12 (02) :155-164

[6] Analysis of finite element approximation of evolution problems in mixed form [J].

Boffi, D ;

Gastaldi, L .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2004, 42 (04) :1502-1526

[7]

BOFFI D., 2013, SPRINGER SER COMPUT, V44, DOI [10.1007/978-3-642-36519-5, DOI 10.1007/978-3-642-36519-5]

[8]

Brezzi F., 2008, Mixed finite elements, compatibility conditions, and applications

[9] Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach [J].

Bukac, M. ;

Yotov, I. ;

Zakerzadeh, R. ;

Zunino, P. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 292 :138-170

[10] DIMENSIONAL MODEL REDUCTION FOR FLOW THROUGH FRACTURES IN POROELASTIC MEDIA [J].

Bukac, Martina ;

Yotov, Ivan ;

Zunino, Paolo .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2017, 51 (04) :1429-1471

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