Numerical Analysis of High Speed Flow Applications using Various Flux Schemes

Abstract

Numerical analysis using computational fluid dynamics is an affordable and effective method with increasing relevance every day in research and engineering problems. Choosing an appropriate convective discretization scheme is paramount importance for obtaining more accurate solutions using CFD methods. The present study compares two commonly used numerical convective schemes, the upwind scheme of Advection Upstream Splitting Method (AUSM) and the central schemes of Kurganov-Noelle-Petrova and Kurganov-Tadmor scheme (K-T) have been made to find the better central scheme. These two schemes are validated with inviscid 1D and 2D problems such as Sod’s shock tube, forward facing step in a Mach 3 tunnel, 15 Degree ramp in a Mach 2 supersonic tunnel, the Mach-reflection problem and scramjet engine operating under high Mach number. The AUSM and K-T schemes are robust enough to capture all the features of compressible flows. Comparison of results obtained by these 2 schemes is presented using density contours and surface property changes. It has been observed that both the schemes are robust enough to capture the flow features of the problems and that they have better accuracy for different conditions.

HIGHLIGHTS

• This paper focuses on two convective flux discretization techniques i.e. the upwind scheme of AUSM and the central schemes of K-T and KNP
• Inviscid simulations for various problems in the supersonic as well as hypersonic regime were used in Sod’s 1-Dimensional Shock Tube, flow over forward facing step in supersonic wind tunnel and Mach 5 flow thorough scramjet engine
• The AUSM and K-T schemes are robust enough to capture all the features of compressible flows. It has been observed that both the schemes are robust enough to capture the flow features of the problems and that they have better accuracy for different conditions

GRAPHICAL ABSTRACT