The performance evaluation of an improved finite volume method that solves the fluid dynamic equations

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. This new scheme, called the Integro-Differential Scheme (IDS), has several favorable qualities. For instance, the scheme is developed based on 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 surfaces 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 different frameworks, such as 1D, quasi 1D and 2D flow problems. The problems of interest to this study are the supersonic cavity flow and the shock wave turbulent boundary layer interaction. A careful analysis of the results generated from the use of the IDS procedure confirms its predictive capabilities and its potential to solve a variety of fluid dynamics problems.