Towards a 3-dimensional phase-field model of non-isothermal alloy solidification

We review the application of advanced numerical techniques such as adaptive mesh refinement, implicit time-stepping, multigrid solvers and massively parallel implementations as a route to obtaining solutions to the 3-dimensional phase-field problem for coupled heat and solute transport during non-isothermal alloy solidification. Using such techniques it is shown that such models are tractable for modest values of the Lewis number (ratio of thermal to solutal diffusivities). Solutions to the 3-dimensional problem are compared with existing solutions to the equivalent 2-dimensional problem.