2-DIMENSIONAL PARALLEL SOLVER FOR THE SOLUTION OF NAVIER-STOKES EQUATIONS WITH CONSTANT AND VARIABLE-COEFFICIENTS USING ADI ON CELLS

The paper proposed a new algorithm for the parallel solution of two-di mensional Navier-Stokes type equation with constant and non-constant c oefficients which is mapped onto cell topology. This paper is a furthe r development in the application of the local Fourier methods to the s olutions of PDE's in multidomain regions. The extension of the above s olution to problems with non-constant coefficients is suggested via sp ectral multidomain preconditioner. This approach is efficient when we have good local approximations in each subdomain. By dividing the comp utational domain into a large enough number of subdomains we can guara ntee it. The new achievement here is that we are able to handle decomp osition of the domain into cells that is the decomposed in both direct ions, x and y. An appropriate alternate direction implicit (ADI) schem e was developed, It enables the reduction of a 2-D problem to a collec tion of uncoupled 1-D ODE's. In effect, the 1-D solver becomes the bas ic routine to solve a 2-D problem using splitting of the differential operators by ADI. Detailed performance analysis is given where the iss ue of the communication among the domains (processors) is examined. We show that by using the Richardson method only local communication is required. The algorithm was implemented on IBM SP2, network of ALPHA w orkstations, and MOSIX [A. Barak, S. Guday, R. Wheeler, The MOSIX Dist ributed Operating System, Load Balancing for UNIX, Lecture Notes in Co mputer Science, Vol. 672, Springer-Verlag, 1993; A. Barak, O. Laden, Z . Yarom, The NOW MOSIX and its Preemptive Process Migration Scheme, IE EE TCOS 7 (2) (1995) 5-11] which is a network of i586. All are impleme nted using the PVM software package and the same ADI program was runni ng on these different multiprocessor configurations. It achieved effic iency of 55-70% depending on the multiprocessor. (C) 1998 Elsevier Sci ence B.V. All rights reserved.