Investigating the Flow Field Physics Within Unsteady Compressible Flows

Abstract

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 an example with 2nd order accuracy in space and 3rd order of accuracy in time. Initial perturbations will lead to bubbles and mushroom-shaped spikes due to the release of potential energy, which is from a linear growth phase into a non-linear growth phase. The Total Variation Diminishing Runge-Kutta (TVD-RK3) 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. Also, IDS Scheme shows its capability to capture more eddies which WENO 5th order is not shown with same computational grids. The IDS simulations are governed by the full set of Navier-Stokes Equations (NES) and focus on the basic flow structure and their interaction which lead to complex flow phenomena. 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. The accuracy and resolution of the unsteady IDS scheme will be tested by its simulations of several benchmark unsteady compressible test cases. Already, evidence of the IDS capability is demonstrated in its simulating solution of the unsteady Rayleigh-Taylor problem.