STEADY-STATE INCOMPRESSIBLE FLOWS USING EXPLICIT SCHEMES WITH AN OPTIMAL LOCAL PRECONDITIONING

Solving large systems of equations from CFD problems by the explicit p seudo-temporal scheme requires a very low amount of memory and is high ly parallelizable, but the CPU time largely depends on the conditionin g of the system. For advective systems it is shown that the rate of co nvergence depends on a condition number defined as the ratio of the ma ximum and the minimum group velocities of the continuum system. If the objective is to reach the steady state, the temporal term can be modi fied in order to reduce this condition number. Another possibility con sists in the addition of a local preconditioning mass matrix. In this paper an optimal preconditioning for incompressible flow is presented, also applicable to compressible ones with locally incompressible zone s, like stagnation points, in contrast with the artificial compressibi lity method. The preconditioned system has a rate of convergence indep endent from Mach number. Moreover, the discrete solution is highly imp roved, eliminating spurious oscillations frequently encountered in inc ompressible flows.