Parallel Solution of a 3-D Mixed Convection Problem

Abstract

As is well known, fully explicit schemes impose severe restrictions on the time step size for analyzing complex viscous flow fields, which are resolved with sufficiently fine grids. To remedy this, implicit flow solvers are used in analyzing such flows. Naturally, the higher order accurate schemes allow one to resolve the flow field with less number of grid points. Resolving the flow field with less number of points gives a great advantage to implicit schemes since the size of the matrix to be inverted becomes small. In this study a second order accurate implicit scheme for solution of full Navier-Stokes equations is developed and implemented. The space is discretized with brick elements while modified version of the two-step fractional method is used in time discretization of the momentum equation. At each time step, the momentum equation is solved only once to get the half time step velocity field. The pressure, on the other hand, is obtained via an auxiliary scalar potential which satisfies the Poisson’ equation. For the parallel implicit solution of the matrix equations, modified version of the Domain Decomposition Method, [1,2,3,4] is utilized, and direct inversion in each domain is performed. Super linear speed-ups were achieved, [5].