A novel algorithm for solving the classical Stefan problem

Abstract

A novel algorithm for solving the classic Stefan problem is proposed in the paper. Instead of front tracking, we preset the moving interface locations and use these location coordinates as the grid points to find out the arrival time of moving interface respectively. Through this approach, the difficulty in mesh generation can be avoided completely. The simulation shows the numerical result is well coincident with the exact solution, implying the new approach performes well in solving this problem.