An Adaptive Finite Volume Methodfor Incompressible Heat FlowProblems in Solidification

An adaptive finite volume method is presented for solving incompressible heat flow problems with an unknown melt/solid interface, mainly in solidification applications, using primitive variables on a fixed collocated grid. A phase-field variable is introduced to treat the melt/solid interface, which is assumed to be diffusive, so that the complicated interfaces and phase change (using the enthalpy model) can be treated easily. The method is implemented through an object-oriented way based on adaptive mesh refinement and coarsening using dynamic data structures and derived data types of FORTRAN90. In addition to the refinement on the interfaces or boundaries, the mesh can be adapted to a solution based on numerical errors or gradients. Extensive tests are performed for cases with a fixed or free interface, and excellent agreement with the body-fitted or front tracking schemes is obtained. Furthermore, by gradual reduction of the interface thickness, the sharp-interface limit can be reached, which ensures the correctness of using a diffusive interface. The present approach is particularly suitable for problems having a complicated interface morphology as well as phase evolution, such as the phase-field simulation of dendritic growth. Two examples, without and with convection, are further given and good agreement with previous results are found. c © 2002 Elsevier Science (USA)