Abstract:
We discuss a mathematical model arising in the melting
of a fluid in two spatial dimensions and in time. The
model leads to a free boundary value problem for
determining the location of the interface as well as the
temperature distribution. The movement of the interface
depends on the temperatures, the velocities and the
material properties at the interface through conditions of
dynamical compatibility for energy transfer. In this
study, we assume that the density and pressure are
constant. A numerical approximation making use of finite
differences and the maximum principle is used to present
existence and uniqueness theorems and continuous
dependence of the solution on the data.
Finally, numerical algorithms for finding approximate
solutions and the results of numerical calculations are
given.
