We derive a multi-component electro-hydro-thermodynamic (EHTD) model for both leaky
and perfect dielectric materials via the principle of energy dissipation. Differing from previous …

In this article, we first establish a new flow-coupled binary phase-field crystal model and
prove its energy law. Then by using some newly introduced variables, we reformulate this …

The two-phase ferrohydrodynamics model consisting of Cahn–Hilliard equations, Navier–
Stokes equations, magnetization equations, and magnetostatic equations is a highly …

A small amount of gas bubbles generated in an on-load tap changer (OLTC) can cause
partial discharges in the intense electric field region, which severely threaten the safe …

A fully decoupled, linearized, and unconditionally stable finite element method is developed
to solve the Cahn–Hilliard–Navier–Stokes–Darcy model in the coupled free fluid region and …

In this paper, we are interested in the design of optimized Schwarz domain decomposition
algorithms to accelerate the Krylov type solution for the Stokes--Darcy system. We use …

In this article, we consider a phase field model with different densities and viscosities for the
coupled two-phase porous media flow and two-phase free flow, as well as the …

In this paper, we first propose and analyze a steady state Dual-Porosity-Navier–Stokes
model, which describes both Dual-Porosity flow and free flow (governed by Navier–Stokes …

In this paper we develop and analyze a variational data assimilation method with efficient
decoupled iterative numerical algorithms for the Stokes–Darcy equations with the Beavers …

In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element
numerical schemes for the Abels-Garcke-Grün (AGG) model, which is a thermodynamically …