PRECONDITIONED ITERATIVE METHODS FOR COUPLED DISCRETIZATIONS OF FLUID-FLOW PROBLEMS

Computational fluid dynamics, where simulations require large computat ion times, is one of the areas of application of high performance comp uting. Schemes such as the SIMPLE (semi-implicit method for pressure-l inked equations) algorithm are often used to solve the discrete Navier -Stokes equations. Generally these schemes take a short time per itera tion but require a large number of iterations. For simple geometries ( or coarser grids) the overall CPU time is small. However, for finer gr ids or more complex geometries the increase in the number of iteration s may be a drawback and the decoupling of the differential equations i nvolved implies a slow convergence of rotationally dominated problems that can be very time consuming for realistic applications. So we anal yze here another approach, DIRECTO, that solves the equations in a cou pled way. With recent advances in hardware technology and software des ign, it became possible to solve coupled Navier-Stokes systems, which are more robust but imply increasing computational requirements (both in terms of memory and CPU time). Two approaches are described here (b and block LU factorization and preconditioned GMRES) for the linear so lver required by the DIRECTO algorithm that solves the fluid flow equa tions as a coupled system. Comparisons of the effectiveness of incompl ete factorization preconditioners applied to the GMRES (generalized mi nimum residual) method are shown. Some numerical results are presented showing that it is possible to minimize considerably the CPU time of the coupled approach so that it can be faster than the decoupled one.