Convergence Acceleration for the Three Dimensional Compressible Navier-Stokes Equations

Abstract

We consider a multistage algorithm to advance in pseudo-time to find a steady state solution for the compressible Navier-Stokes equations. The rate of convergence to the steady state is improved by using an implicit preconditioner to approximate the numerical scheme. This properly addresses the stiffness in the discrete equations associated with highly stretched meshes. Hence, the implicit operator allows large time steps i.e. CFL numbers of the order of 1000. The proposed method is applied to three dimensional cases of viscous, turbulent flow around a wing, achieving dramatically improved convergence rates