Massively parallel finite element computations of three-dimensional, time-dependent, incompressible flows in materials processing systems Original Research Article

A parallel implementation of the Galerkin finite element method for three-dimensional, incompressible flows is presented. The inherent element-by-element parallelism of the method is exploited to make efficient use of the architecture of the CM-5 computer. Our implementation features a mixed formulation to expand the primitive variables using triquadratic brick elements with linear, discontinuous pressure basis functions, and the GMRES method with diagonal preconditioning is employed to solve the linear system at each Newton iteration. Transitions among flow states in the classical Taylor-Couette system, which are representative of the complexity of flows found in materials processing systems, are computed as benchmark solutions, and preliminary results are presented for flow in a large-scale, solution crystal growth system. Sustained calculation rates of up to 6 GigaFLOPS are achieved on 512 processors of the CM-5.