Computational Fluid Dynamics (CFD) continues to play a critical role in the solution of complex fluid dynamics flows. This computational tool allows us to investigate complex flow patterns that would otherwise be impossible to investigate and has greatly aided in the development of our knowledgebase. At the Heart of successful CFD tools are creative numerical schemes that are developed and used in an attempt to capture ‘real world’ flow physics. One such creative numerical scheme in the Integro-Differential Scheme (IDS) has be created. In previous studies, the IDS Scheme has demonstrated that it has achieved adequate dispersion and dissipation capabilities in the smooth flow field regions along with very robust shock-capturing capabilities in the vicinity of discontinuities. In this proposed paper, the IDS Scheme will focus on unsteady fluid motion like Rayleigh-Taylor Instability problem as a with 2nd order accuracy in space and 3rd order of accuracy in time. The TVD-RK3 (Total Variation Diminishing Runge-Kutta Scheme) will be applied in IDS Scheme and shows incredible results. The detail of how eddies are formatting and interact will be proposed in this paper.&nbsp; Also, IDS Scheme shows its capability to capture more eddies which WENO 5th order is not shown with same computational grids. The IDS simulations will focus on the compressible ﬂows typically known for their ability include complex flow physics and governed by the full set of Navier–Stokes’s equations (NSE). The numerical form of the IDS to be used for solving these compressible flow field problems will consist of the coupled 3rd order Runge-Kutta explicit time marching method and an explicit spatial integral method for the control volume convective ﬂux evaluation. In general, the order of the spatial and temporal schemes is independent of each other. The accuracy and resolution of the unsteady IDS scheme will be tested by its simulations of several benchmark unsteady compressible test cases. The performance of this scheme will be further demonstrated by its application in the direct numerical simulation of the compressible separation bubble over an isothermal wall flat-plate. The problem of major interest to this study is the capturing of the separation bubble on a Flat-plate at Mach one half and Reynolds number of one million. There is existing confidence of the IDS capability in simulating the unsteady Rayleigh-Taylor problem, and its ability to capture the basic fluid physics. In addition, there are plans to simulate many of the unsteady Riemann problems. With limited results from contact discontinuity solutions, The IDS Scheme shows it has the capability to catch up Kelvin-Helmholtz Instabilities know as K-H Instability with increase of grid density.

Investigating the Flow Field Physics Within Unsteady Compressible Flows

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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