Godunov Method For Stefan Problems With Neumann And Robin Type Boundary Condition Using Dimensionless Enthalpy Formulation

A Stefan problem is a boundary value problem where the position of one of the boundaries is time-dependent. In this article, we consider one-dimensional phase-change Stefan problems where the fixed boundary is Neumann-type and Robin-type. We solve the problem using a numerical approach by deriving dimensionless enthalpy formulation based on suitable finite difference approximation. Numerical schema is obtained by applying the Godunov method on the formulation. We use several cases of various functions for boundary conditions and small initial conditions. The result obtained provide important information to develop a currently unavailable exact solution or another approximation solution.