The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply a prediction-projection method that transforms the Navier-Stokes equations into three Helmholtz equations and one Poisson equation. For each Helmholtz system, we apply the Alternating Direction Implicit (ADI) method resulting in three tridiagonal systems. The Poisson equation is solved using partial diagonalization which transforms the Laplacian operator into a tridiagonal one. We present an implementation based on MPI where the computations are performed on each subdomain and information is exchanged at the interfaces between subdomains. We describe in particular how the solution of tridiagonal systems can be accelerated using vectorization techniques.
A parallel solver for incompressible fuid flows