MASSIVELY-PARALLEL FINITE-ELEMENT COMPUTATIONS OF 3-DIMENSIONAL, TIME-DEPENDENT, INCOMPRESSIBLE FLOWS IN MATERIALS PROCESSING SYSTEMS

A parallel implementation of the Galerkin finite element method for th ree-dimensional, incompressible flows is presented. The inherent eleme nt-by-element parallelism of the method is exploited to make efficient use of the architecture of the CM-5 computer. Our implementation feat ures a mixed formulation to expand the primitive variables using triqu adratic brick elements with linear, discontinuous pressure basis funct ions, and the GMRES method with diagonal preconditioning is employed t o solve the linear system at each Newton iteration. Transitions among flow states in the classical Taylor-Couette system, which are represen tative of the complexity of flows found in materials processing system s, are computed as benchmark solutions, and preliminary results are pr esented for flow in a large-scale, solution crystal growth system. Sus tained calculation rates of up to 6 GigaFLOPS are achieved on 512 proc essors of the CM-5.