A moving-mesh finite element method and itsudapplication to the numerical solution of phase-changeudproblems

摘要

A distributed Lagrangian moving-mesh finite element method is applied to problemsudinvolving changes of phase. The algorithm uses a distributed conservation principle to de-udtermine nodal mesh velocities, which are then used to move the nodes. The nodal values areudobtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a gener-udalisation of the original algorithm presented in Applied Numerical Mathematics, 54:450–469ud(2005). Having described the details of the generalised algorithm it is validated on two testudcases from the original paper and is then applied to one-phase and, for the first time, two-udphase Stefan problems in one and two space dimensions, paying particular attention to theudimplementation of the interface boundary conditions. Results are presented to demonstrateudthe accuracy and the effectiveness of the method, including comparisons against analyticaludsolutions where available.