Crystal growth and dendritic solidification
Journal of Computational Physics
A front-tracking method for dendritic solidification
Journal of Computational Physics
Journal of Computational Physics
An Adaptive Mesh Projection Method for Viscous Incompressible Flow
SIAM Journal on Scientific Computing
A simple level set method for solving Stefan problems
Journal of Computational Physics
Multiphase dynamics in arbitrary geometries on fixed Cartesian grids
Journal of Computational Physics
Finite-volume CFD procedure and adaptive error control strategy for grids of arbitrary topology
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
Journal of Computational Physics
Multigrid methods for incompressible heat flow problems with an unknown interface
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
Modeling melt convection in phase-field simulations of solidification
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
Application of adaptive mesh refinement method to complex flows in clean rooms
International Journal of Computational Fluid Dynamics
Hi-index | 31.45 |
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.