A parallel finite element method for incompressible Navier–Stokes flows based on unstructured grids

Abstract This paper presents a parallel finite element method for the large scale computation of incompressible Navier–Stokes flows using unstructured grids. The streamline upwind/Petrov–Galerkin (SUPG) formulation is employed to improve the numerical stability and accuracy and the pressure stabilization matrix (PSM) is introduced to avoid the occurrence of the checkerboard pressure mode. For the finite element, the velocity-tri-linear/pressure-piecewise constant (Q1/P0) element is employed. The pressure Poisson equation is parallelized with the element-by-element scaled conjugate gradient (SCG) method. Parallel implementation of the unstructured-grid-based formulation is carried out on the Hitachi Parallel Computer SR2201. The effect of parallelization on the efficiency of the computations is examined.

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