Data parallel finite element techniques for largescale computational fluid dynamics
Abstract
The objective of this work is to address two major issues arising in the computation of largescale flow problems: storage and computing cost. A Galerkin/leastsquares finite element formulation is used to solve the compressible NavierStokes equations. Structural heating is also considered by performing a classical Galerkin finite element discretization and by having a fully implicit coupling with the fluid. A matrix free implicit iterative solver based on the Generalized Minimal Residual Algorithm (GMRES) is developed to solve the nonlinear system of equations arising from the finite element discretizations. It is shown that the performance of this solver compares favorably with traditional implicit iterative techniques while reducing substantially the memory requirements. The computing cost issue is addressed through a data parallel implementation of the finite element solver on the Connection Machine massively parallel computers. A blocking strategy is presented to facilitate the handling of several element types in the same mesh. Two communication algorithms performing the gather and scatter operations required by the finite element implementation are proposed. The first algorithm makes use of communication primitives available in the Connection Machine Scientific Software Library. The second algorithm preserves data locality by partitioning the mesh using a parallel implementation of the spectral partitioning algorithm. The mesh decomposition leads to a reduction in the amount of data to be communicated between processing nodes. Fluidstructural heating interaction problems and compressible flow problems using meshes with close to one million elements, such as flow over a complete airplane, demonstrate the efficiency of the data parallel computing and communication strategies.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT........19J
 Keywords:

 Computational Fluid Dynamics;
 Costs;
 Finite Element Method;
 NavierStokes Equation;
 Parallel Processing (Computers);
 Algorithms;
 Compressible Flow;
 Connection Machine;
 Galerkin Method;
 Interprocessor Communication;
 Nonlinear Equations;
 Fluid Mechanics and Heat Transfer