Simulations of single-and multi-species compressible flows with shock waves and discontinuities are conducted using a weighted compact nonlinear scheme (WCNS) with a newly developed sixth order localized dissipative interpolation. In smooth regions, the scheme applies the central nonlinear interpolation with minimum dissipation to resolve fluctuating flow features while in regions containing discontinuities and high wavenumber features, the scheme

The interaction of a Mach 1.45 shock wave with a perturbed planar interface between sulphur hexafluoride and air is studied through high-resolution two-dimensional (2D) and three-dimensional (3D) shock-capturing adaptive mesh refinement simulations of multi-species Navier-Stokes equations. The sensitivities of time-dependent statistics on grid resolution for 2D and 3D simulations are evaluated to ensure the accuracy of the results. The numerical results are used to examine the differences between the development of 2D and 3D Richtmyer-Meshkov instability during two different stages: (1) initial growth of hydrodynamic instability from multi-mode perturbations after first shock and (2) transition to chaotic or turbulent state after re-shock. The effects of the Reynolds number on the mixing in 3D simulations are also studied through varying the transport coefficients. * wongml@stanford.edu † livescu@lanl.gov ‡

No abstract

We present an improved high-order weighted compact high resolution (WCHR) scheme that extends the idea of weighted compact nonlinear schemes (WCNS's) using nonlinear interpolations in conjunction with compact finite difference schemes for shock-capturing in compressible turbulent flows. The proposed scheme has better resolution property than previous WCNS's. This is achieved by using a compact (or spatially implicit) form instead of the traditional fully explicit form for the nonlinear interpolation. Since compact interpolation schemes tend to have lower dispersion errors compared to explicit interpolation schemes, the proposed scheme has the ability to resolve more fine-scale features while still having the ability to provide sufficiently localized dissipation to capture shocks and discontinuities robustly. Approximate dispersion relation characteristics of this scheme are analyzed to show the superior resolution properties of the scheme compared to other WCNS's of similar orders of accuracy. Conservative and high-order accurate boundary schemes are also proposed for non-periodic problems. Further, a new conservative flux-difference form for compact finite difference schemes is derived and allows for the use of positivity-preserving limiters for improved robustness. Different test cases demonstrate the ability of this scheme to capture discontinuities in a robust and stable manner while also localizing the required numerical dissipation only to regions containing discontinuities and very high wavenumber features and hence preserving smooth flow features better in comparison to WCNS's.