PARALLEL FINITE-ELEMENT COMPUTATION OF UNSTEADY INCOMPRESSIBLE FLOWS

A parallel semi-explicit iterative finite element computational proced ure for modelling unsteady incompressible fluid flows is presented. Du ring the procedure, element flux vectors are calculated in parallel an d then assembled into global flux vectors. Equilibrium iterations whic h introduce some 'local implicitness' are performed at each time step. The number of equilibrium iterations is governed by an implicitness p arameter. The present technique retains the advantages of purely expli cit schemes, namely (i) the parallel speed-up is equal to the number o f parallel processors if the small communication overhead associated w ith purely explicit schemes is ignored and (ii) the computation time a s well as the core memory required is linearly proportional to the num ber of elements. The incompressibility condition is imposed by using t he artificial compressibility technique. A pressure-averaging techniqu e which allows the use of equal-order interpolations for both velocity and pressure, this simplifying the formulation, is employed. Using a standard Galerkin approximation, three benchmark steady and unsteady p roblems are solved to demonstrate the accuracy of the procedure. In al l calculations the Reynolds number is less than 500. At these Reynolds numbers it was found that the physical dissipation is sufficient to s tabilize the convective term with no need for additional upwind-type d issipation. (C) 1998 John Wiley & Sons, Ltd.