Development of an all speed navier-stokes preconditioner for two and three dimensional flows on hybrid grids

Baş, Onur
In this study, a novel Mach uniform preconditioning method is developed for the solution of Euler/Navier-Stokes equations at subsonic and incompressible flow conditions. In contrast to the methods developed earlier in which the conservation of mass equation is preconditioned, the conservation of energy equation is preconditioned in the present method to enforce the divergence free constraint on the velocity field even at the limiting case of incompressible, zero Mach number flows. The proposed Mach-uniform preconditioning method does not have a singularity point at zero free-stream Mach number. The modified system of equations preserves the strong conservation form of the governing equations for compressible flows and recovers the artificial compressibility equations in the case of zero Mach number. Two and three dimensional preconditioned solvers are developed for validation and performance evaluation of the present formulation on a wide range of Mach number flows. The studied cases show the convergence acceleration, stability and accuracy of the present Mach uniform preconditioner in comparison to the non-preconditioned compressible flow solutions. The convergence acceleration achieved is similar to those of the well known preconditioned system of equations for low subsonic flows and to the artificial compressibility method for incompressible flows.