A Moving-Mesh Finite Element Method and Its Application to the Numerical Solution of Phase-Change Problems (Communications in Computational Physics, 2009)
A distributed Lagrangian moving-mesh finite element method is applied toproblems involving changes of phase. The algorithm uses a distributed conservationprinciple to determine nodal mesh velocities, which are then used to move the nodes.The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation,which represents a generalization of the original algorithm presented in AppliedNumerical Mathematics, 54:450–469 (2005). Having described the details of the generalizedalgorithm it is validated on two test cases from the original paper and is thenapplied to one-phase and, for the first time, two-phase Stefan problems in one and twospace dimensions, paying particular attention to the implementation of the interfaceboundary conditions. Results are presented to demonstrate the accuracy and the effectivenessof the method, including comparisons against analytical solutions whereavailable.