A parallelization study designed for ADI-type algorithms is presented using the OpenMP specification for shared-memory multiprocessor programming. Details of optimizations specifically addressed to cache-based computer architectures are described and performance measurements for the single and multiprocessor implementation are summarized. The paper demonstrates that optimization of memory access on a cache-based computer architecture controls the performance of the computational algorithm. A hybrid MPI/OpenMP approach is proposed for clusters of shared memory machines to further enhance the parallel performance. The method is applied to develop a new LES/DNS code, named LESTool. A preliminary DNS calculation of a fully developed channel flow at a Reynolds number of 180, Re(sub tau) = 180, has shown good agreement with existing data.Hauser, Th. and Huang, P. G.Glenn Research CenterMULTIPROCESSING (COMPUTERS); PARALLEL PROCESSING (COMPUTERS); MEMORY (COMPUTERS); COMPUTER PROGRAMS; PARALLEL PROGRAMMING; ALGORITHMS; ARCHITECTURE (COMPUTERS); OPTIMIZATION; REYNOLDS NUMBER; FORTRAN; CHANNEL FLOW; NAVIER-STOKES EQUATION; COMPUTATIONAL FLUID DYNAMICS...