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In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant…
In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the…
Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable.…
An alternative to the fully implicit or monolithic methods used for the solution of the coupling of fluid flow and deformation in porous media is a sequential approach in which the fully coupled system is broken into subproblems (flow and…
The computational analysis of fiber network fracture is an emerging field with application to paper, rubber-like materials, hydrogels, soft biological tissue, and composites. Fiber networks are often described as probabilistic structures of…
Equation systems resulting from a p-version FEM discretisation typically require a special treatment as iterative solvers are not very efficient here. Applying hierarchical concepts based on a nested dissection approach allow for both the…
The accurate, reliable and efficient numerical approximation of multi-physics processes in heterogeneous porous media with varying media coefficients that include fluid flow and structure interactions is of fundamental importance in energy,…
We propose three semi-decoupled algorithms for efficiently solving a four-field thermoporoelastic model. The first two algorithms adopt a sequential strategy: at the initial time step, all variables are computed simultaneously using a…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
In this work, we present the construction of two distinct finite element approaches to solve the Porous Medium Equation (PME). In the first approach, we transform the PME to a log-density variable formulation and construct a continuous…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
Heuristic algorithms have shown a good ability to solve a variety of optimization problems. Stockpile blending problem as an important component of the mine scheduling problem is an optimization problem with continuous search space…
We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also referred to as MPET models. The focus of the paper is on the…
In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with…
This paper introduces a unified model for thermo-poroelasticity and multiple-network poroelasticity, reformulated into a total-pressure-based system. We first establish the well-posedness of the problem via a Galerkin-based argument and…
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…
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…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and…
We present a fully implicit formulation of coupled fluid flow and geomechanics for fluid injection/withdrawal in fractured reservoirs in the context of CO2storage. Utilizing a Galerkin finite-element approach, both flow and poroelasticity…