An Evaluation of Coupled Fluid-Thermal Numerical Schemes for Moving Phase Boundaries in ElmerFEM

This paper presents an evaluation of a transient, coupled multiphysics Finite Element Method(FEM) framework using an Arbitrary Lagrangian–Eulerian (ALE) mesh update to model moving solid-gas phase boundaries governed by the Stefan condition. The architecture couples fivesolvers sequentially within a BDF2 temporal loop: HeatSolve, FluxSolver, MeshSolve, AdvectionDiffusion, and FlowSolve. As a representative test case, the sublimation of carbon dioxide(dry ice) within constrained geometries is evaluated using this architecture.Transient 2D simulations over a 1500-second duration show that the coupled scheme remainsstable under boundary heater temperatures of 300 K, 400 K, and 1000 K, capturing the highvelocity transient settling of the solvers before the gas velocities relax. However, geometricvariations reveal limits: restricting the gaseous domain size remains stable (Case 1) for over300 s, but further altering the shape of the boundary contours (Case 2) causes solver halt at20 s.Expanding the framework to 3D by increasing the degrees of freedom (DOFs) leads to rapiddivergence. Even with a simplified flat boundary, the 3D model (Stefan3D1.sif) crashes at2.7 s due to an escalation of the interface fluid velocity, which peaks at 3.1 m/s. Future workmust focus on 3D durability.