Implicit multigrid solution of the preconditioned multi-dimensional Euler equations

Abstract

A new local preconditioning method based on the concept of artificial compressibility has been developed to accelerate the convergence to steady state solutions of the Euler equations of inviscid, compressible flow at low Mach numbers. An extension of the method to a matrix preconditioning which is effective over the range of Mach numbers from subsonic through low supersonic is also presented. The numerical results demonstrate that convergence rate is independent of Mach number in the range 10~5 < M < 0.6 while a significant improvement in convergence rate is also achieved in the transonic regime. In addition to the convergence benefits, the results also indicate that the preconditioning significantly reduces the numerical dissipation leading to more accurate solutions. The improvement in solution accuracy is more pronounced in the incompressible limit where the conventional algorithms are known to be inaccurate.