Parallel simulation of fluid flow inside the rotating cylindrical container on the Intel Paragon

The parallelization of Fourier spectral and Chebyshev collocation methods to the cylindrical form of the Navier-Stokes equations with one periodic and two nonperiodic directions has been implemented. The matrix diagonalization technique, which has been applied to solve the elliptic equations which occur in the implicit steps of the three-step time-splitting algorithm, enables one to parallelize only the matrix-matrix multiplication routines. The parallel matrix multiplication algorithms of Cannon and Fox have thus been explored and compared with each other in detail. A speedup of up to 3.7 has been obtained on the Intel Paragon parallel computer as compared with the CRAY Y-MP vector computer.