Finite Difference Simulations of the Navier-Stokes Equations using Parallel Distributed Computing

This paper discusses the implementation of a numerical algorithm for simulating incompressible fluid flows based on the finite difference method and designed for parallel computing platforms with distributed-memory, particularly for clusters of workstations. The solution algorithm for the Navier-Stokes equations utilizes an explicit scheme for pressure and an implicit scheme for velocities, i. e., the velocity field at a new time step can be computed once the corresponding pressure is known. The parallel implementation is based on domain decomposition, where the original calculation domain is decomposed into several blocks, each of which given to a separate processing node. All nodes then execute computations in parallel, each node on its associated sub-domain. The parallel computations include initialization, coefficient generation, linear solution on the subdomain, and inter-node communication. The exchange of information across the sub-domains, or processors, is achieved using the message passing interface standard, MPI. The use of MPI ensures portability across different computing platforms ranging from massively parallel machines to clusters of workstations. The execution time and speed-up are evaluated through comparing the performance of different numbers of processors. The results indicate that the parallel code can significantly improve prediction capability and efficiency for large-scale simulations