Modelling of Phase Change With Non-Constant Density Using Xfem and a Lagrange Multiplier

Abstract

A two phase model for two-dimensional solidification problems with variable densities was developed by coupling the Stefan problem with the Stokes problem and applying a mass conserving velocity condition on the phase change interface. The extended finite element method (XFEM) was used to capture the strong discontinuity of the velocity and pressure as well as the jump in heat flux at the i nterface. The melting temperature and velocity condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration a lgorithm. Three examples were investigated and the results were compared to numerical results coming from a commercial software using ALE techniques to track the solid/liquid interface. The model was able to reproduce the benchmark simulations while maintaining a sharp phase change interface and conserving mass.

Fluid-structure interaction: Extended-FEM approach to solidification

“…Stapor [28] considered the density difference in driving the melt flow but made no hydrodynamic calculation. The final addition of the hydrodynamic calculation with buoyancy was applied in Martin et al [29,30], but the methodology made no enrichment in the approximation of the velocity and pressure fields. It was not until Li et al [31] that XFEM with LSM coupled the Stefan and hydrodynamic problems and considered non-constant density phase changes and buoyancy effects.…”