Low speed preconditioning for an unstructured grid Navier-Stokes solver

Abstract

A computational flow solution procedure suitable for low speed flows has been demonstrated. The new capability has been developed within the framework of tetrahedral unstructured grid-based Navier-Stokes solver USMSD, originally developed for the compressible flow applications. A widely followed approach of local preconditioning has been adopted for this purpose. The method modifies the time derivatives of the system of governing equations by multiplying them with a suitable preconditioning matrix such that eigenvalues of the system remain well conditioned for the low speed. The preconditioner matrix of Weiss and Smith has been chosen for this purpose. The assessment of the new capability has been performed by computations on several simplified configurations representative of the complex flow problems routinely encountered. Initially, a very low speed laminar flow over a flat plate has been studied and the computed velocity profile compared with the Blasius solution. Subsequently, turbulent flow over ONERA wing is analyzed in the Mach number range of 0.2-0.01 and convergence characteristics as well as solution insensitivity to the Mach number in the low speed regime is highlighted. Next, low Mach number and high angle-of-attack turbulent flow computations are performed for NACA 4412 airfoil and a wing with partial-span flap. The computed surface pressures are compared with the respective experimental investigations. Lastly, validity of the enhanced solver for high speed compressible flow has been demonstrated by considering turbulent transonic flow over ONERA wing and comparing the computed and measured surface pressures. Results demonstrate the applicability of the code for the broader regime of the flow speed.