Primitive variable, strongly implicit calculation procedure for viscous flows at all speeds

Abstract

A coupled solution procedure is described for solving the compressible form of the time-dependent, twodimensional Navier-Stokes equations in body-fitted curvilinear coordinates. This approach employs the strong conservation form of the governing equations but uses primitive variables (M, v, p, T) rather than the more traditional conservative variables (p, pw, pv, et) as unknowns. A coupled modified strongly implicit procedure (CMSIP) is used to efficiently solve the Newton-linearized algebraic equations. It appears that this procedure is effective for Mach numbers ranging from the incompressible limit (Mx ~ 0.01) to supersonic. Generally, smoothing was not needed to control spatial oscillations in pressure for subsonic flows despite the use of central differences. Dual-time stepping was found to further accelerate convergence for steady flows. Sample calculations, including steady and unsteady low-Mach-number internal and external flows and a steady shock-boundarylayer interaction flow, illustrate the capability of the present solution algorithm.