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This paper presents the numerical solution of immiscible two-phase flows in porous media, obtained by a first-order finite element method equipped with mass-lumping and flux up-winding. The unknowns are the physical phase pressure and phase…
In energy science, Darcy flow in heterogeneous porous media is a central problem in reservoir sim-ulation. However, the pronounced multiscale characteristics of such media pose significant challenges to conventional numerical methods in…
We develop a numerical scheme for a two-phase immiscible flow in heterogeneous porous media using a structured grid finite element method, which have been successfully used for the computation of various physical applications involving…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
We present a hybrid framework that couples finite element methods (FEM) with physics-informed DeepONet to model fluid transport in porous media from sharp, localized Gaussian sources. The governing system consists of a steady-state Darcy…
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 numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…
A mathematical model for computation of the fluid pressure in a reservoir drained by a horizontal multiple fractured well is proposed. The model is applicable for an arbitrary network of fractures with different finite conductivities of…
An industrial scheme, to simulate the two compressible phase flow in porous media, consists in a finite volume method together with a phase-by-phase upstream scheme. The implicit finite volume scheme satisfies industrial constraints of…
While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…
The emergence and understanding of new design paradigms that exploit flow induced mechanical instabilities for propulsion or energy harvesting demands robust and accurate flow structure interaction numerical models. In this context, we…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…
Robust and accurate fully implicit finite-volume schemes applied to Darcy-scale multiphase flow and transport in porous media are highly desirable. Recently, a smooth approximation of the saturation-dependent flux coefficients based on…
Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element…
In this paper we study a Darcy-scale mathematical model for biofilm formation in porous media. The pores in the core are divided into three phases: water, oil, and biofilm. The water and oil flow are modeled by an extended version of…
A weighted residual collocation methodology for simulating two-dimensional shear-driven and natural convection flows has been presented. Using a dyadic mesh refinement, the methodology generates a basis and a multiresolution scheme to…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…