Weighted Essentially Non-Oscillatory Simulations and Modeling of Complex Hydrodynamic Flows. Part 2. Single-Mode Richtmyer-Meshkov Instability with Reshock

Download or read book Weighted Essentially Non-Oscillatory Simulations and Modeling of Complex Hydrodynamic Flows. Part 2. Single-Mode Richtmyer-Meshkov Instability with Reshock written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Richtmyer-Meshkov instability is a fundamental fluid instability that occurs when perturbations on an interface separating gases with different properties grow following the passage of a shock. This instability is typically studied in shock tube experiments, and constitutes a fundamental example of a complex hydrodynamic flow. Numerical simulations and models for the instability growth and evolution have also been used to further elucidate the physics of the Richtmyer-Meshkov instability. In the present work, the formally high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method using a third-order total-variation diminishing (TVD) Runge-Kutta time-evolution scheme (as implemented in the HOPE code [68]) is applied to simulate the single-mode Richtmyer-Meshkov instability with reshock in two spatial dimensions. The initial conditions and computational domain for the simulations are modeled after the Collins and Jacobs [29] single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment. The following boundary conditions are used: (1) periodic in the spanwise direction corresponding to the cross section of the test section; (2) outflow at the entrance of the test section in the streamwise direction, and; (3) reflecting at the end wall of the test section in the streamwise direction. The present investigation has three principal motivations: (1) to provide additional validation of the HOPE code against available experimental data; (2) to provide numerical simulation data for detailed analysis of mixing induced by the Richtmyer-Meshkov instability with reshock, and; (3) to systematically investigate the dependence of mixing properties on both the order of WENO reconstruction and on the spatial resolution. The present study constitutes the first comprehensive application of the high-resolution WENO method to the Richtmyer-Meshkov instability with reshock, as well as analysis of the resulting mixing.