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This article describes the porting and optimization of an explicit,time-dependent, computational fluid dynamics code on an 8,192-nodeMasPar MP-1. The MasPar is a very fine-grained, single instruction,multiple data parallel computer. The code uses the flux-correctedtransport algorithm. We describe the techniques used to port andoptimize the code, and the behavior of a test problem. The testproblem used to benchmark the flux-corrected transport code on theMasPar was a two-dimensional exploding shock with periodic boundaryconditions. We discuss the performance that our code achieved onthe MasPar, and compare its performance on the MasPar with itsperformance on other architectures. The comparisons show that theperformance of the code on the MasPar is slightly better than on aCRAY Y-MP for a functionally equivalent, optimized two-dimensionalcode.