Related papers: Mechanics-based solution verification for porous m…
We analyze a non-isothermal Darcy-Brinkman thin-film flow with a periodically oscillating boundary and viscous dissipation acting as a heat source. Using asymptotic analysis and the periodic unfolding method, we establish the convergence of…
In this paper, we present a residual-driven multiscale method for simulating Darcy flow in perforated domains, where complex geometries and highly heterogeneous permeability make direct simulations computationally expensive. To address…
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous…
There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus.…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
In this work, we analyze the flow filtration process of slightly compressible fluids in porous media containing man made fractures with complex geometries. We model the coupled fracture-porous media system where the linear Darcy flow is…
This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on…
In the flow and transport numerical simulation, mesh adaptivity strategy is important in reducing the usage of CPU time and memory. The refinement based on the pressure error estimator is commonly-used approach without considering the flux…
We perform linear and nonlinear stability analysis for thermal convection in a fluid overlying a saturated porous medium. We use a coupled system, with the Navier-Stokes equations and Darcy's equation governing the free-flow and the porous…
We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy-Forchheimer law while that in the surrounding matrix is governed by Darcy's law. We give an appropriate mixed,…
In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a…
We experimentally examine pressure-driven flows of 1%, 3%, and 5% dilute suspensions over and through a porous media model. The flow of non-colloidal, non-Brownian suspensions of rigid and spherical particles suspended in a Newtonian fluid…
It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
The paper presents a numerical method for simulating flow and mechanics in fractured rock. The governing equations that couple the effects in the rock mass and in the fractures are obtained using the discrete fracture-matrix approach. The…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
We show the existence of infinitely many admissible weak solutions for the incompressible porous media equations for all Muskat-type initial data with $C^{3,\alpha}$-regularity of the interface in the unstable regime and for all…
This article presents a detailed introduction to density-based topology optimisation of fluid flow problems. The goal is to allow new students and researchers to quickly get started in the research area and to skip many of the initial…
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…
Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores, which is commonly referred to as double porosity. To…