TY - JOUR
T1 - Godunov Method for Stefan Problems with Enthalpy Formulations
AU - D. Tarwidi & S.R. Pudjaprasetya
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 107
EP - 119
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.030513.200513a
UR - https://global-sci.org/intro/article_detail/eajam/10850.html
KW - Stefan problems, Godunov method, solidification, enthalpy, cryosurgery.
AB - <p style="text-align: justify;">A Stefan problem is a free boundary problem where a phase boundary moves
as a function of time. In this article, we consider one-dimensional and two-dimensional
enthalpy-formulated Stefan problems. The enthalpy formulation has the advantage that
the governing equations stay the same, regardless of the material state (liquid or solid).
Numerical solutions are obtained by implementing the Godunov method. Our simulation
of the temperature distribution and interface position for the one-dimensional
Stefan problem is validated against the exact solution, and the method is then applied
to the two-dimensional Stefan problem with reference to cryosurgery, where extremely
cold temperatures are applied to destroy cancer cells. The temperature distribution and
interface position obtained provide important information to control the cryosurgery
procedure.</p>