The Performance Evaluation of an Improved Finite Volume Method for Solving the Navier Stokes Equation

One of the most important goals of this research effort is to improve the efficiencies of computational fluid dynamic (CFD) tools by focusing on the development of a robust and accurate numerical framework capable of solving the Navier-Stokes Equations under a wide variety of initial and boundary conditions. The new scheme, which was initially described in Ref. 1 and referred to as the Integro-Differential Scheme (IDS), has a number of favorable qualities. For instance, the scheme is developed on the basis of a unique combination of the differential and integral forms of the Navier-Stokes Equations (NSE). In this paper, the differential form of the NSE is used for explicit time marching and the integral form is used for spatial flux evaluations. As such, the scheme has the potential to accurately capture the complex physics of fluid flows. In addition, the Method of Consistent Averages (MCA) numerical procedure directly provides continuity of the numerical flux quantities rather than manipulating the primitive flowfield variables to ensure continuity. Coupled temporal and spatial analyses of the mass, momentum, and energy fluxes are considered at two major locations; namely, at the center of the numerical control volume, and at each of the surface making up an elementary control volume. It is also of interest to note that the IDS procedure developed herein is based on two fundamental types of control volumes. This paper elaborates on the development of the IDS procedure and presents the results of its implementation on three established fundamental high Reynolds number fluid dynamic problems. The problems of interest to this study are the supersonic rearward facing step and the supersonic cavity flow problems. A careful analysis of the results generated from the use of the IDS procedure confirms its predictive capability and supports its potential to solve a variety of fluid dynamics problems.