| Abstract: | A Stefan problem is a free boundary problem where a phase boundary movesas a function of time. In this article, we consider one-dimensional and two-dimensionalenthalpy-formulated Stefan problems. The enthalpy formulation has the advantage thatthe governing equations stay the same, regardless of the material state (liquid or solid).Numerical solutions are obtained by implementing the Godunov method. Our simulationof the temperature distribution and interface position for the one-dimensionalStefan problem is validated against the exact solution, and the method is then appliedto the two-dimensional Stefan problem with reference to cryosurgery, where extremelycold temperatures are applied to destroy cancer cells. The temperature distribution andinterface position obtained provide important information to control the cryosurgeryprocedure. |
