A Mach-uniform preconditioner for incompressible and subsonic flows

Abstract

In this study, a novel Mach-uniform preconditioning method is developed for the solution of Euler equations at low subsonic and incompressible flow conditions. In contrast to the methods developed earlier in which the conservation of mass equation is preconditioned, in the present method, the conservation of energy equation is preconditioned, which enforces the divergence free constraint on the velocity field even at the limiting case of incompressible, zero Mach number flows. Despite most preconditioners, the proposed Mach-uniform preconditioning method does not have a singularity point at zero Mach number. The preconditioned system of equations preserves the strong conservation form of Euler equations for compressible flows and recovers the artificial compressibility equations in the case of zero Mach number. A two-dimensional Euler solver is developed for validation and performance evaluation of the present formulation for a wide range of Mach number flows. The validation cases studied 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 obtained with the present formulation is similar to those of the well-known preconditioned system of equations for low subsonic flows and to those of the artificial compressibility method for incompressible flows. Copyright (c) 2013 John Wiley & Sons, Ltd.