Improving Initial Guess for the Iterative Solution of Linear Equation Systems in Incompressible Flow

Abstract

The pressure equation, generated while solving the incompressible Navier−Stokes equations with the segregated iterative algorithm such as PISO, produces a series of linear equation systems as the time step advances. In this paper, we target at accelerating the iterative solution of these linear systems by improving their initial guesses. We propose a weighted group extrapolation method to obtain a superior initial guess instead of a general one, the solution of the previous linear equation system. In this method, the previous solutions that are used to extrapolate the predicted solutions are carefully organized to address the oscillatory solution on each grid. The proposed method uses a weighted average of the predicted solutions as the new initial guess to avoid over extrapolating. Three numerical test results show that the proposed method can accelerate the iterative solution of most linear equation systems and reduce the simulation time up to 61.3%.

Keywords

• incompressible navier–stokes equations
• segregated iterative algorithm
• linear equation system
• initial guess
• iterative method