Smoothed Particle Hydrodynamics Method for Two-dimensional Stefan Problem

TL;DR

This paper develops a two-dimensional smoothed particle hydrodynamics method to model melting and solidification processes, using the enthalpy method to handle heat transfer and phase change interfaces.

Contribution

It introduces a novel SPH approach for simulating melting/solidification with phase separation strategy and applies it to model floating ice melting in water.

Findings

Numerical simulations successfully depict melting dynamics.

The method effectively handles moving phase interfaces.

Results vary with different initial conditions.

Abstract

Smoothed particle hydrodynamics (SPH) is developed for modelling of melting and solidification. Enthalpy method is used to solve heat conduction equations which involved moving interface between phases. At first, we study the melting of floating ice in the water for two-dimensional system. The ice objects are assumed as solid particles floating in fluid particles. The fluid and solid motion are governed by Navier-Stokes equation and basic rigid dynamics equation, respectively. We also propose a strategy to separate solid particles due to melting and solidification. Numerical results are obtained and plotted for several initial conditions.