An implicit regularized enthalpy Lattice Boltzmann Method for the Stefan problem
Numerical Analysis
2025-05-20 v1 Numerical Analysis
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.
Cite
@article{arxiv.2505.13097,
title = {An implicit regularized enthalpy Lattice Boltzmann Method for the Stefan problem},
author = {Francky Luddens and Corentin Lothodé and Ionut Danaila},
journal= {arXiv preprint arXiv:2505.13097},
year = {2025}
}