An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
Development of a 2-D algorithm to simulate convection and phase transition efficiently
Journal of Computational Physics
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Solidifying flow equations can be used to model industrial metallurgical processes such as casting and welding, and material science applications such as crystal growth. These flow equations contain locally stiff nonlinearities at the moving phase-change interface. We are developing a three-dimensional parallel simulation tool for such problems using a Jacobian-free Newton--Krylov solver and unstructured finite volume methods. A segregated (distributed, block triangular) preconditioning strategy is being developed for the Newton--Krylov solver. In this preconditioning approach we are only required to approximately invert matrices coming from a single field variable, not matrices arising from a coupled system. Additionally, simple linearizations are used in constructing our preconditioning operators. The preconditioning strategy is presented along with the performance of the methods. We consider problems in phase-change heat transfer and the thermally driven incompressible Navier--Stokes equations separately. This is a required intermediate step toward developing a successful preconditioning strategy for the fully coupled physics problem.