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In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…

Numerical Analysis · Mathematics 2021-04-27 Kevin Chow , Steven J. Ruuth

We analyze an iterative coupling of mixed and discontinuous Galerkin methods for numerical modelling of coupled flow and mechanical deformation in porous media. The iteration is based on an optimized fixed-stress split along with a…

Numerical Analysis · Mathematics 2018-02-12 Markus Bause

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the…

Numerical Analysis · Mathematics 2024-02-19 Ryan M. Aronson , Nicola Castelletto , François P. Hamon , J. A. White , Hamdi A. Tchelepi

We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative…

Numerical Analysis · Mathematics 2020-09-21 Benjamin Rüth , Benjamin Uekermann , Miriam Mehl , Philipp Birken , Azahar Monge , Hans-Joachim Bungartz

In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities and/or small time steps. We consider different…

Numerical Analysis · Mathematics 2024-07-30 Álvaro Pé de la Riva , Francisco J. Gaspar , Xiaozhe Hu , James Adler , Carmen Rodrigo , Ludmil Zikatanov

In this paper, we study the numerical algorithm for a nonlinear poroelasticity model with nonlinear stress-strain relations. By using variable substitution, the original problem can be reformulated to a new coupled fluid-fluid system, that…

Numerical Analysis · Mathematics 2022-05-17 Zhihao Ge , Hairun Li , Tingting Li

The paper studies a time-nonlocal multiphysics finite element method with Crank-Nicolson scheme for poroelasticity model with secondary consolidation. For the case where the physical parameters $\lambda,\lambda^*$ and $c_0$ are all finite…

Numerical Analysis · Mathematics 2026-04-09 Zhihao Ge , Yanan He

An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…

Fluid Dynamics · Physics 2013-01-22 Alessandro Iafrati

Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange…

Fluid Dynamics · Physics 2022-06-30 Nicholas J. Derr , Chris H. Rycroft

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

Many applications from geosciences require simulations of seismic waves in porous media. Biot's theory of poroelasticity describes the coupling between solid and fluid phases and introduces a stiff source term, thereby increasing…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-03-02 Sebastian Wolf , Martin Galis , Carsten Uphoff , Alice-Agnes Gabriel , Peter Moczo , David Gregor , Michael Bader

In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field…

Numerical Analysis · Mathematics 2017-09-07 Sanghyun Lee , Thomas Wick , Mary F. Wheeler

We study the dynamics of the solid to liquid transition for a model material made of elastic particles immersed in a viscous fluid. The interaction between particle surfaces includes their viscous lubrication, a sharp repulsion when they…

Fluid Dynamics · Physics 2015-05-14 P. Rognon , I. Einav , C. Gay

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

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

In this paper, we propose a parallel solver for solving the quasi-static linear poroelasticity coupled with linear elasticity model in the Lagrange multiplier framework. Firstly, we reformulate the model into a coupling of the nearly…

Numerical Analysis · Mathematics 2025-09-09 Zhihao Ge , Chengxin Wang

In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…

Numerical Analysis · Mathematics 2016-09-23 Lorenz Berger

The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a stabilizing term to the flow equation, which includes a…

Numerical Analysis · Mathematics 2021-05-24 Erlend Storvik , Jakub Wiktor Both , Jan Martin Nordbotten , Florin Adrian Radu

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

Numerical Analysis · Mathematics 2025-07-22 Markus Bachmayr , Matthieu Dolbeault , Polina Sachsenmaier

Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…

Numerical Analysis · Mathematics 2024-09-27 Marcus J. Grote , Simon R. J. Michel , Stefan A. Sauter