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We study a high order finite difference scheme to solve the time accurate flow field of a jet using the compressible Navier-Stokes equations. As part of our ongoing efforts, we have implemented our numerical model on three parallel computing platforms to study the computational, communication, and scalability characteristics. The platforms chosen for this study are a cluster of workstations connected through fast networks (the LACE experimental testbed at NASA Lewis), a shared memory multiprocessor (the Cray YMP), and a distributed memory multiprocessor (the IBM SPI). Our focus in this study is on the LACE testbed. We present some results for the Cray YMP and the IBM SP1 mainly for comparison purposes. On the LACE testbed, we study: (1) the communication characteristics of Ethernet, FDDI, and the ALLNODE networks and (2) the overheads induced by the PVM message passing library used for parallelizing the application. We demonstrate that clustering of workstations is effective and has the potential to be computationally competitive with supercomputers at a fraction of the cost.