Solution of One-Dimensional Stefan Problem with Orthogonal Collocation
A Stefan problem is a boundary value problem for a partial differential equation in which a phase boundary can move with time. An orthogonal collocation method is used in this Demonstration to solve the one-dimensional Stefan problem with periodic boundary condition.
Consider the one-dimensional Stefan problem with periodic Dirichlet boundary condition. The diferential equation for this nonlinear problem, expressed in dimensionless form, is given by
subject to initial and boundary conditions
This problem has applications in heat and mass transfer, for example, the melting of ice, recrystallization of metals, evaporation of droplets, etc.
Reference: S. Savovic and J. Caldwell, "Finite Difference Solution of One Dimensional Stefan Problem with Periodic Boundary Conditions," International Journal of Heat and Mass Transfer, 46(15), 2003 pp. 2911–2916.