相关论文: Predicting nonlinear-flow regions in highly hetero…
We show that the widely used model governing the motion of two incompressible immiscible fluids in a possibly heterogeneous porous medium has a formal gradient flow structure. More precisely, the fluid composition is governed by the…
In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element…
An outstanding characteristic of porous media, desired in many applications, is the large surface area, which facilitates solid-fluid interactions, making porous media an extreme case in colloid and interface science. In two-fluid systems,…
We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a…
We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…
This paper is focused on the generalized Forchheimer flows of slightly compressible fluids in porous media. They are reformulated as a degenerate parabolic equation for the pressure. The initial boundary value problem is studied with…
Darcy's law and the Brinkman equation are two main models used for creeping fluid flows inside moving permeable particles. For these two models, the time derivative and the nonlinear convective terms of fluid velocity are neglected in the…
Fluid infiltration of a permeable brick in contact with a pressurized reservoir of fluid is considered. A stochastic model, informed by Darcy's law and the incompressibility of the fluid, shows how the heterogeneity of the permeability…
We study the slightly compressible Darcy-Forchheimer equations modeling gas flow in porous media, particularly in applications related to combustion processes. The equations are discretized in time using the backward Euler method and in…
The work investigates a model that combines a convection-diffusion-reaction equation for solute concentration with an unsteady Darcy-Brinkman equation for the flow field, including the Kortweg stress. Additionally, the flow field…
In this paper, we extend the Darcy law for micropolar fluid flow in a thin porous medium. This provides a framework for understanding how a fluid's microstructural properties, the geometry of the porous medium and the thickness of the…
Most organic liquids exhibit a pressure-dependent viscosity, making it crucial to consider this behavior in applications where pressures significantly exceed ambient conditions (e.g., geological carbon sequestration). Mathematical models…
Direct numerical simulation of Stokes flow through an impermeable, rigid body matrix by finite elements requires meshes fine enough to resolve the pore-size scale and is thus a computationally expensive task. The cost is significantly…
This paper is focused on the generalized Forchheimer flows of compressible fluids in porous media. The gravity effect and other general nonlinear forms of the source terms and boundary fluxes are integrated into the model. It covers…
In this paper, we are concerned with the simulation of blood flow in microvascular networks and the surrounding tissue. To reduce the computational complexity of this issue, the network structures are modeled by a one-dimensional graph,…
Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic…
Porous membranes are thin solid structures that allow the flow to pass through their tiny openings, called pores. Flow inertia may play a significant role in several filtration flows of natural and engineering interest. Here, we develop a…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with…
This paper develops the a priori analysis of a mixed finite element method for the filtration of an incompressible fluid through a non-deformable saturated porous medium with heterogeneous permeability. Flows are governed by the…