An implicit regularized enthalpy Lattice Boltzmann Method for the Stefan problem

TL;DR

This paper introduces a regularized enthalpy Lattice Boltzmann Method for the Stefan problem, effectively handling phase change with high accuracy and scalability through a nonlinear Newton solver and theoretical analysis.

Contribution

It develops a novel Lattice Boltzmann scheme for the Stefan problem using a regularized total enthalpy model with nonlinear source terms, analyzed via Chapman-Enskog expansion.

Findings

High accuracy in 1D and 2D benchmarks

Scalable due to local problem conservation

Effective handling of nonlinear phase change dynamics

Abstract

Solving the Stefan problem, also referred as the heat conduction problem with phase change, is a necessary step to solve phase change problems with convection. In this article, we are interested in using the Lattice Boltzmann Method (LBM) to solve the Stefan problem using a regularized total enthalpy model. The liquid fraction is treated as a nonlinear source/sink term, that involves the time derivative of the solution. The resulting non-linear system is solved using a Newton algorithm. By conserving the locality of the problem, this method is highly scalable, while keeping a high accuracy. The newly developed scheme is analyzed theoretically through a Chapman-Enskog expansion and illustrated numerically with 1D and 2D benchmarks.