A 3D Navier-Stokes solution algorithm is being developed and implemented. The algorithm, which currently solves laminar flow but is to be extended in the near future to perform large eddy simulations, assumes a 2D geometry and periodic flow in the transverse direction. With these assumptions, a combined finite-element/spectral discretization is well suited, with the in-plane discretization being finite-element and the transverse discretization being spectral. This discretization technique, along with explicit treatment of the convective terms, results in a transformation of the 3D problem to a set of 2D problems that are completely decoupled within each time step, greatly decreasing the computational cost and allowing for parallelization without grid partitioning.

This work originated as a 9-month Diploma Course research project at the von Karman Institute for Fluid Dynamics in Rhode-St.-Gen,se, Belgium. It is now being continued as doctoral dissertation research at Utah State University, where the use of an 8-processor Origin 2000 supercomputer has been allocated. A typical large eddy simulation using this solver will require thousands of time steps, each involving the solution of on the order of 64 linear systems containing 80,000 degrees of freedom. Consequently, an efficient and robust linear system solution algorithm designed to take advantage of sparse, block-structured system matrices is necessary. In addition, highly optimized algorithms to perform Fourier transforms and various large matrix and vector manipulations are essential.