We propose a novel second order in time numerical scheme for Cahn–Hilliard–Navier–
Stokes phase field model with matched density. The scheme is based on second order …

In this paper, we consider the numerical approximation for a phase field model of the
coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn …

In this article a domain decomposition method is proposed to solve a time-dependent Navier-
Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary …

This paper proposes and analyzes a Robin-type multiphysics domain decomposition
method (DDM) for the steady-state Navier--Stokes--Darcy model with three interface …

In this paper, we propose a diffuse interface model and finite element approximation for two-
phase magnetohydrodynamic (MHD) flows with different viscosities and electric …

In this article we consider the numerical modeling and simulation via the phase field
approach for coupled two-phase free flow and two-phase porous media flow of different …

We propose and analyze an efficient ensemble algorithm with artificial compressibility (AC)
for fast decoupled computation of multiple realizations of the stochastic Stokes‐Darcy model …

We analyze a fully discrete finite element numerical scheme for the Cahn–Hilliard–Stokes–
Darcy system that models two-phase flows in coupled free flow and porous media. To avoid …

In this article, we present a time-dependent dual-porosity–Navier–Stokes model with four
interface conditions, including Beavers–Joseph interface condition, to describe a coupling …

We study the well-posedness of a coupled Cahn–Hilliard–Stokes–Darcy system which is a
diffuse-interface model for essentially immiscible two phase incompressible flows with …