An iterative domain decomposition method for free boundary problems with nonlinear flux jump constraint

TL;DR

This paper introduces an iterative domain decomposition method for free boundary problems with nonlinear flux jumps, utilizing finite element implementation and harmonic mesh deformation, demonstrated on fluid and magnetohydrodynamics models.

Contribution

It presents a novel iterative scheme for free boundary problems with nonlinear flux constraints, incorporating harmonic mesh deformation for efficient finite element analysis.

Findings

The method converges effectively on jet flow and magnetohydrodynamics models.

Finite element implementation with harmonic meshes reduces computational costs.

Numerical examples confirm the scheme's convergence and robustness.

Abstract

In this paper we design an iterative domain decomposition method for free boundary problems with nonlinear flux jump condition. Our approach is related to damped Newton's methods. The proposed scheme requires, in each iteration, the approximation of the flux on (both sides of) the free interface. We present a Finite Element implementation of our method. The numerical implementation uses harmonically deformed triangulations to inexpensively generate finite element meshes in subdomains. We apply our method to a simplified model for jet flows in pipes and to a simple magnetohydrodynamics model. Finally, we present numerical examples studying the convergence of our scheme.