A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model

DOI10.1007/s00211-018-0967-1zbMath1406.76081arXiv1710.06750OpenAlexW2963610160MaRDI QIDQ1616016

Ilona Ambartsumyan, Paolo Zunino, Eldar Khattatov, Ivan Yotov

Publication date: 31 October 2018

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.06750

zbMATH Keywords

robustnesserror estimatesstability analysisfinite elementsLagrange multipliernumerical experimentswell-posednessmixed finite elementsinf-sup conditioncouplingStokes equationnon-matching gridsinterface conditionsRaviart-Thomasbackward Eulerfractured reservoirBeavers-Joseph-Saffman conditionfully discrete formulationLadyzhenskaya-Babuska-Brezzi conditionsemidiscrete caseBiot sytemDarcy formulationeffect of deformationfree fluidMINI elementsporoelastic structureTaylor-Hood

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (42)

A posteriori error estimates for a nonconforming finite element discretization of the Stokes-Biot system ⋮ A mixed elasticity formulation for fluid–poroelastic structure interaction ⋮ Nonconforming finite element methods for a Stokes/Biot fluid-poroelastic structure interaction model ⋮ A refined two-scale model for newtonian and non-Newtonian fluids in fractured poroelastic media ⋮ A consistent computational approach for general fluid-poroelasticity-structure-contact interaction problems ⋮ A dimensionally-reduced fracture flow model for poroelastic media with fluid entry resistance and fluid slip ⋮ A three-field Banach spaces-based mixed formulation for the unsteady Brinkman-Forchheimer equations ⋮ A finite element scheme for the numerical solution of the Navier-Stokes/Biot coupled problem ⋮ Direct simulation \textit{vs} subgrid scale modelling of fluid flow in fractured or fracturing porous media ⋮ Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers ⋮ A Nitsche-based cut finite element method for the coupling of incompressible fluid flow with poroelasticity ⋮ A posteriori error analysis for a Lagrange multiplier method for a Stokes/Biot fluid-poroelastic structure interaction model ⋮ The locking-free finite difference method based on staggered grids for the coupled Stokes–Biot problem ⋮ A Study of Numerical Pollution of the Decoupled Algorithm for the Convection Model in Superposed Fluid and Porous Layers ⋮ A multipoint stress-flux mixed finite element method for the Stokes-Biot model ⋮ Decoupled modified characteristic finite element method for the time‐dependent Navier–Stokes/Biot problem ⋮ Numerical analysis of the coupling of free fluid with a poroelastic material ⋮ Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem ⋮ Rational approximation preconditioners for multiphysics problems ⋮ Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials ⋮ A staggered finite element procedure for the coupled Stokes-Biot system with fluid entry resistance ⋮ A stable pressure-correction MAC scheme for the fluid-Poroelastic material interaction problem ⋮ Flux-mortar mixed finite element methods with multipoint flux approximation ⋮ Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity ⋮ A semi-decoupled MAC scheme for the coupled fluid-poroelastic material interaction ⋮ Hybridizable discontinuous Galerkin methods for the coupled Stokes-Biot problem ⋮ A decoupled stabilized finite element method for the time–dependent Navier–Stokes/Biot problem ⋮ A Cell-Centered Finite Volume Method for the Navier–Stokes/Biot Model ⋮ Multigrid Methods for Discrete Fractional Sobolev Spaces ⋮ Assembly of Multiscale Linear PDE Operators ⋮ Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot's consolidation model ⋮ Multilayered Poroelasticity Interacting with Stokes Flow ⋮ Biot-pressure system with unilateral displacement constraints ⋮ Mathematical analysis and numerical approximation of a general linearized poro-hyperelastic model ⋮ A nonlinear Stokes–Biot model for the interaction of a non-Newtonian fluid with poroelastic media ⋮ The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye ⋮ Flow and transport in fractured poroelastic media ⋮ On mathematical and numerical modelling of multiphysics wave propagation with polytopal discontinuous Galerkin methods: a review ⋮ A Next-Generation Mathematical Model for Drug-Eluting Stents ⋮ Numerical Modeling of the Fluid-Porohyperelastic Structure Interaction ⋮ Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media ⋮ A High-Order Discontinuous Galerkin Method for the Poro-elasto-acoustic Problem on Polygonal and Polyhedral Grids

Uses Software

• FreeFem++
• MMMFEM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid
• Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility
• Implementation of a mortar mixed finite element method using a multiscale flux basis
• Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction
• Domain decomposition for coupled Stokes and Darcy flows
• Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations
• The narrow fracture approximation by channeled flow
• Modeling fractures as interfaces: A model for Forchheimer fractures
• Cardiovascular mathematics. Modeling and simulation of the circulatory system
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• A numerical solution of the Navier-Stokes equations using the finite element technique
• Phase-field modeling of a fluid-driven fracture in a poroelastic medium
• Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach
• Mathematical and numerical models for coupling surface and groundwater flows
• Theory and practice of finite elements.
• Fluid-structure interactions. Models, analysis and finite elements
• A Darcy-Brinkman model of fractures in porous media
• A multiscale Darcy-Brinkman model for fluid flow in fractured porous media
• Mortar multiscale finite element methods for Stokes-Darcy flows
• Fluid-structure interaction. Modelling, simulation, optimisation. Proceedings of the workshop, Hohenwart, Germany, October 2005
• Asymptotic Analysis of the Laminar Viscous Flow Over a Porous Bed
• A mixed finite element method for Darcy flow in fractured porous media with non-matching grids
• Convergence analysis of a new mixed finite element method for Biot's consolidation model
• Pressure jump interface law for the Stokes–Darcy coupling: confirmation by direct numerical simulations
• Simulation of Flow in Fractured Poroelastic Media: A Comparison of Different Discretization Approaches
• Explicit strategies for incompressible fluid-structure interaction problems: Nitsche type mortaring versus Robin-Robin coupling
• Nonlinear Degenerate Evolution Equations in Mixed Formulation
• On the Boundary Condition at the Surface of a Porous Medium
• An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure
• Numerical modelling of multiphase subsurface flow in the presence of fractures
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• DG Approximation of Coupled Navier–Stokes and Darcy Equations by Beaver–Joseph–Saffman Interface Condition
• Coupling Fluid Flow with Porous Media Flow
• Locally Conservative Coupling of Stokes and Darcy Flows
• Computational Fluid–Structure Interaction
• Mixed Finite Element Methods and Applications
• New development in freefem++
• Fundamental Trends in Fluid-Structure Interaction
• A lubrication fracture model in a poro-elastic medium
• Modeling Fractures and Barriers as Interfaces for Flow in Porous Media
• Dimensional model reduction for flow through fractures in poroelastic media
• A Multiscale Mortar Mixed Finite Element Method

This page was built for publication: A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model