The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method
The authors describe and analyze a new numerical method for solving the multiphase Stefan problem for a general nonlinear one-dimensional heat conduction equation. They reformulate the problem using an enthalpy function and use a semi-implicit moving mesh discretization to approximate the resulting weak formulation. The discontinuities in the enthalpy-temperature relation are smoothed as a part of this process. The mesh modification strategy allows then smooth evolution of mesh nodes to track the interfaces. The system of nonlinear algebraic equations at each time step is shown to possess a unique solution and solved by Newton's method. Numerical experiments with two examples are described in detail showing good performance of the method. No unphysical staircase behaviour of the phase interfaces (common with using fixed uniform meshes in the enthalpy formulations) is observed here. Extensions of the methodology for problems in more than one dimension are shortly discussed in the end of the paper.
scientific article; zbMATH DE number 1496457
scientific article