To deal with such multi-scale problems we have applied a range of advanced numerical techniques, such as dynamic mesh adaptivity, implicit time-stepping and a non-linear multigrid solver to phase-field modes that solve for the coupled diffusion of both heat and solute in 2- and 3- dimension. In addition, our 3-dimensional code employs parallel processing with dynamic load balancing in order to take advantage of High Performance Computing (HPC) facilities. Both the 2- and 3-dimensional models are formulated in the ‘thin-interface’ limit and as such are capable of yielding quantitatively correct results. Some examples of simulated dendrite morphologies, and the meshes used to perform the simulations, are shown below.
Example of a growing dendrite and an adapting mesh in 2-dimensions.
The 2-dimensional code, PhAIM-2d (Phase-field by Adaptive Implicit Multigrid in 2-dimensions) used to generate the simulations above is available as an Open Source download from the Leeds software repository.
PhAIM-2d was developed in c and should run on most Linux machines supporting the Atlas and Blas libraries. The open-source package is freely available for any non-commercial purpose. The 3-dimensional version will be released as an Open Source package when development, debugging and validation work is complete.
Prof. A.M. Mullis