Composite adaptive grid generation, migration and parallel algorithms for computational materials processing

Solid-liquid phase change problems are encountered in many physico-chemical phenomena and materials processes. The presence of unknown free surfaces and moving interfaces that may be non-planar together with irregular system boundaries complicates the analysis of these processes. Modeling and simulation of such complex processes, require a robust adaptive grid generation scheme, particularly suitable for moving boundary problems, a generalized flow solver for transport equations with special treatment for free and moving interfaces, and an efficient parallel algorithm that can exploit the latest developments in computing hardware and software.; In this work, a Composite Adaptive Grid Generation and Migration (CAGGM) scheme that is specially suitable for irregular system with free and moving interfaces has been developed for both two- and three-dimensional systems. CAGGM allows to generate multiblock composite adaptive grids by dividing a multiphase system into a number of non-conforming structured grid blocks. A Multiphase Adaptive Grid Generation and Migration (MAGGM) scheme has also been formulated and implemented to improve the grid characteristics and solution accuracy for changing area/volume of the subdomains through grid addition/deletion that is based on a number of solution criteria. To improve the performance of the calculations, flow solvers based on the generalized Navier-Stokes equations have been developed and specifically adapted to the non-conforming CAGGM scheme. The mismatched grid interfaces require higher order localized interpolation algorithms to satisfy the conservation equations and solution physics. A reduction in computation time is accomplished through a generalized parallel algorithm with spatial domain decomposition approach. The parallel algorithm consists of two major components: (1) parallel adaptive grid generation and (2) parallel flow solver through curvilinear non-orthogonal finite volume approach. Currently, the parallel algorithm is developed for only two-dimensional problems.; The numerical algorithms and solution strategies have been implemented and tested for selected application problems like solidification/melting in a rectangular cavity and low and high pressure Czochralski crystal growth. It Is shown that the CAGGM scheme and the parallel algorithm with the associated flow solvers can be effectively used for a broad class of complex materials processing problems and other phase-change phenomena with improved computation time and better numerical accuracy.