Related papers: Computational multiscale methods for linear hetero…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…
Significant progress has been made for assessing the influence of porosity on the performance metrics for cast components through various modeling techniques. However, a computationally efficient framework to account for porosity with…
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…
We propose a model for the coupling between free fluid and a linearized poro-hyperelastic body. In this model, the Brinkman equation is employed for fluid flow in the porous medium, incorporating inertial effects into the fluid dynamics. A…
The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the…
Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to…
We consider a multicontinuum model in porous media applications, which is described as a system of coupled flow equations. The coupling between different continua depends on many factors and its modeling is important for porous media…
Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…
We consider the coupled system of equations that describe flow in fractured porous media. To describe such types of problems, multicontinuum and multiscale approaches are used. Because in multicontinuum models, the permeability of each…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
A phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects is considered. The pore-scale model consists of a strongly coupled system of Stokes-Cahn-Hilliard equations. The fluids are…
The large-deformation mechanics and multiphysics of continuous or fracturing partially saturated porous media under static and dynamic loads are significant in engineering and science. This article is devoted to a computational coupled…
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…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
We quantify the numerical error and modeling error associated with replacing a nonlinear nonlocal bond-based peridynamic model with a local elasticity model or a linearized peridynamics model away from the fracture set. The nonlocal model…
In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…