Preconditioning Newton-Krylov methods in solidifying flow applications

Solidifying flow equations can be used to model industrial metallurgical pr ocesses such as casting and welding, and material science applications such as crystal growth. These flow equations contain locally sti nonlinearities at the moving phase-change interface. We are developing a three-dimensiona l parallel simulation tool for such problems using a Jacobian-free Newton K rylov solver and unstructured finite volume methods. A segregated ( distrib uted, block triangular) preconditioning strategy is being developed for the Newton Krylov solver. In this preconditioning approach we are only require d to approximately invert matrices coming from a single field variable, not matrices arising from a coupled system. Additionally, simple linearization s are used in constructing our preconditioning operators. The preconditioni ng strategy is presented along with the performance of the methods. We cons ider problems in phase-change heat transfer and the thermally driven incomp ressible Navier Stokes equations separately. This is a required intermediat e step toward developing a successful preconditioning strategy for the full y coupled physics problem.