Reformulated formulation and efficient fully discrete finite element method for a conductive ferrofluid model

TL;DR

This paper introduces a new, efficient finite element method for simulating conductive ferrofluids, combining reformulated equations and stability techniques to handle complex multiphysics interactions.

Contribution

It presents a decoupled, linear, second-order, energy stable finite element scheme with rigorous solvability and stability proofs for conductive ferrofluid modeling.

Findings

Scheme is unconditionally energy stable.

Numerical examples confirm accuracy and efficiency.

Method effectively handles nonlinear, coupled equations.

Abstract

In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear, and multiphysics system efficiently, we develop a decoupled, linear, second-order in time, and unconditionally energy stable finite element scheme. We incorporate several distinct numerical techniques, including reformulations of the equations and a scalar auxiliary variable to handle the coupled nonlinear terms,a symmetric implicit-explicit treatment for the symmetric positive definite nonlinearity, and stable finite element approximations. We also prove that the numerical scheme is provably uniquely solvable and unconditionally energy stable rigorously. A series of numerical examples are presented to illustrate the accuracy and performance of our scheme.