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We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…

Numerical Analysis · Mathematics 2021-06-09 Andrea Borio , François Hamon , Nicola Castelletto , Joshua A. White , Randolph R. Settgast

In this paper, we propose a numerical method for computing solutions to Biot's fully dynamic model of incompressible saturated porous media [Biot;1956]. Our spatial discretization scheme is based on the three-field formulation (u-w-p) and…

Numerical Analysis · Mathematics 2015-06-24 Zahrasadat Lotfian , Mettupalayam Sivaselvan

This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative…

Numerical Analysis · Mathematics 2018-10-11 Saumik Dana , Mary F. Wheeler

A quasi-static filtration system, comprising a poroelastic solid coupled to an incompressible free-flow, is considered in 3D. Across a flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. The system constitutes a…

Analysis of PDEs · Mathematics 2026-05-15 Peter Lavagnino , Arum Lee , Justin T. Webster

In this paper, we propose a multiphysics mixed finite element method with Nitsche's technique for Stokes-poroelasticity problem. Firstly, we present a multiphysics reformulation of poroelasticity part of the original problem by introducing…

Numerical Analysis · Mathematics 2021-12-24 Zhihao Ge , Jin'ge Pang , Jiwei Cao

This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…

Numerical Analysis · Mathematics 2025-04-29 Salim Meddahi

Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…

Numerical Analysis · Mathematics 2021-05-24 Jakub W. Both , Kundan Kumar , Jan M. Nordbotten , Iuliu Sorin Pop , Florin A. Radu

In this paper we consider the development of Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such systems the scaling depends on an additional parameter which modifies the nature of the…

Numerical Analysis · Mathematics 2017-01-17 S. Boscarino , L. Pareschi , G. Russo

In this paper we develop adaptive iterative coupling schemes for the Biot system modeling coupled poromechanics problems. We particularly consider the space-time formulation of the fixed-stress iterative scheme, in which we first solve the…

Numerical Analysis · Mathematics 2024-12-20 Elyes Ahmed , Jan Martin Nordbotten , Florin Adrian Radu

We consider a fully discrete loosely coupled scheme for incompressible fluid-structure interaction based on the time semi-discrete splitting method introduced in {\emph{[Burman, Durst \& Guzm\'an, arXiv:1911.06760]}}. The splittling method…

Numerical Analysis · Mathematics 2020-07-09 Erik Burman , Rebecca Durst , Miguel A. Fernández , Johnny Guzmán

We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…

Numerical Analysis · Mathematics 2023-07-19 Martina Bukac , Ivan Yotov , Rana Zakerzadeh , Paolo Zunino

We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is…

Numerical Analysis · Mathematics 2010-09-16 L. Pareschi , G. Russo

We investigate a coupled hyperbolic-parabolic system modeling thermoelastic diffusion (resp. thermo-poroelasticity) in plates, consisting of a fourth-order hyperbolic partial differential equation for plate deflection and two second-order…

Numerical Analysis · Mathematics 2025-06-18 Neela Nataraj , Ricardo Ruiz-Baier , Aamir Yousuf

Fully implicit timestepping methods have several potential advantages for atmosphere/ocean simulation. First, being unconditionally stable, they degrade more gracefully as the Courant number increases, typically requiring more solver…

Numerical Analysis · Mathematics 2025-10-16 Werner Bauer , Colin J. Cotter

We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…

Numerical Analysis · Mathematics 2026-01-21 Amy de Castro , Hyesuk Lee

This work considers simultaneous homogenization dimension reduction of a poroelastic model for thin fiber-reinforced hydrogels. The analysed medium is defined as a two-component system consisting of a continuous fiber framework with…

Analysis of PDEs · Mathematics 2026-02-03 Amartya Chakrabortty , Haradhan Dutta , Hari Shankar Mahato

The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or…

Numerical Analysis · Mathematics 2020-10-20 Eleonora Piersanti , Jeonghun J. Lee , Travis Thompson , Kent-Andre Mardal , Marie E. Rognes

We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been…

Numerical Analysis · Mathematics 2020-01-01 Herbert Egger , Mania Sabouri

We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacement and the Darcy velocity are approximated by discontinuous…

Numerical Analysis · Mathematics 2022-07-27 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

We consider the efficient numerical solution of coupled dynamical systems, consisting of a small nonlinear part and a large linear time invariant part, possibly stemming from spatial discretization of an underlying partial differential…

Numerical Analysis · Mathematics 2018-11-27 Herbert Egger , Vsevolod Shashkov , Kersten Schmidt