A Multi-resolution particle method with high order accuracy for solid-liquid phase change represented by sharp moving interface

Wang, Z. ; Sugiyama, Tomoyuki ; Matsunaga, Takuya*; Koshizuka, Seiichi*

This paper develops a highly accurate, multi-resolution particle method to simulate solid-liquid phase change coupled with the thermal flow. Instead of including the latent heat in the governing equation, the heat equations for solid and liquid phases are solved separately. A sharp interface model is proposed to represent the solid-liquid interface explicitly. The sharp interface, represented by discrete nodes, provides the Neumann boundary condition for pressure and the Dirichlet boundary condition for velocity/temperature, respectively. Based on temperature gradients in the solid and liquid phases, the positions of these interface nodes are updated every time step. The Eulerian-based formulation, rather than the conventional Lagrangian-based one, is utilized to minimize time step-dependent error. Up to 4th order spatial discretization scheme is adopted based on the Least Square Moving Particle Semi-implicit (LSMPS) scheme. Moreover, a geometry-based multi-resolution scheme is introduced to dynamically refine the spatial resolution near the interface for saving computational cost. The 1-D Stefan problem is firstly simulated to verify the accuracy of the proposed sharp interface model. Then, the consistency of the multi-resolution scheme is investigated by a convergence study of the Taylor-Green vortex problem. After that, numerical simulations of natural convection in a cavity are performed with different spatial resolutions and high order schemes. Resulted computational costs are compared and discussed. Finally, the problems of melting by natural convection with different Rayleigh numbers are investigated. The results achieved so far indicate that the multi-resolution and high order schemes have great potential to save computational cost.