Weak and strong solutions for a fluid‐poroelastic‐structure interaction via a semigroup approach

G Avalos, E Gurvich, JT Webster - Mathematical Methods in the …, 2024 - Wiley Online Library
A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes
free‐flow is considered in 3D. Across the flat 2D interface, the Beavers‐Joseph‐Saffman …

Mathematical effects of linear visco-elasticity in quasi-static Biot models

L Bociu, B Muha, JT Webster - Journal of Mathematical Analysis and …, 2023 - Elsevier
We investigate and clarify the mathematical properties of linear poro-elastic systems in the
presence of classical (linear, Kelvin-Voigt) visco-elasticity. In particular, we quantify the time …

Fixed stress splitting approach for contact problems in a porous medium

T Almani, K Kumar - arxiv preprint arxiv:2407.13459, 2024 - arxiv.org
We consider a poromechanics model including frictionless contact mechanics. The resulting
model consists of the Biot equations with contact boundary conditions leading to a …

Semilinear Degenerate Biot–Signorini System

A Hosseinkhan, RE Showalter - SIAM Journal on Mathematical Analysis, 2023 - SIAM
Nonlinear extensions of the quasi-static Biot model of consolidation are studied with
emphasis on boundary conditions, attainment of initial values, and parabolic regularizing …

Numerical solution of the Biot/elasticity interface problem using virtual element methods

S Kumar, D Mora, R Ruiz-Baier, N Verma - Journal of Scientific Computing, 2024 - Springer
We propose, analyse and implement a virtual element discretisation for an interfacial
poroelasticity/elasticity consolidation problem. The formulation of the time–dependent …

The Mathematical Effects of Visco-elasticity in Quasi-static Biot Models

L Bociu, B Muha, JT Webster - UMBC Faculty Collection, 2022 - mdsoar.org
We investigate and clarify the mathematical properties of linear poro-elastic systems
(quasistatic Biot) with the addition of classical visco-elasticity. We precisely demonstrate the …

The Biot System with Unilateral Displacement Constraints

A Hosseinkhan - 2022 - ir.library.oregonstate.edu
A fully-saturated poroelastic medium is confined by the sides of a cylinder, and the regions
below and above the medium are filled with fluid at respective constant pressures. The …