Numerical simulations of a shock interacting with successive interfaces using the Discontinuous Galerkin method: the multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities

Abstract

In this work, we investigate the growth of interface perturbations following the interaction of a shock wave with successive layers of fluids. Using the Discontinuous Galerkin method, we solve the two-dimensional multifluid Euler equations. In our setup, a shock impacts up to four adjacent fluids with perturbed interfaces. At each interface, the incoming shock generates reflected and transmitted shocks and rarefactions, which further interact with the interfaces. By monitoring perturbation growth, we characterize the influence these instabilities have on each other and the fluid mixing as a function of time in different configurations. If the third gas is lighter than the second, the reflected rarefaction at the second interface amplifies the growth at the first interface. If the third gas is heavier, the reflected shock decreases the growth and tends to reverse the Richtmyer-Meshkov instability as the thickness of the second gas is increased. We further investigate the effect of the reflected waves on the dynamics of the small scales and show how a phase difference between the perturbations or an additional fluid layer can enhance growth. This study supports the idea that shocks and rarefactions can be used to control the instability growth.

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces

“…Gmsh is used for the mesh generation and post-processing visualization [59]. Our code has been used previously to simulate the multilayered Richtmyer-Meshkov and Rayleigh-Taylor instabilities [60] and experiments of blast-wave-driven shear flow in high-energy-density regimes [61].…”

Evolution of shock-accelerated heavy gas layer

“…The Evolution of shock-accelerated heavy gas layer 886 A7-3 effects of initial conditions such as the amplitude and wavelength of the interface on late-time RM instability evolution were considered. Numerically, the interaction of a shock wave with successive layers of fluids was investigated by de Frahan, Movahed & Johnsen (2015), and the effects of initial amplitude, relative phase and distance between interfaces on the amplitude growth were discussed. The authors also considered the effect of RT instability involved in the light/heavy/light fluid layer case.…”

Convergent Richtmyer–Meshkov instability of a heavy gas layer with perturbed outer interface

“…The co-evolution of two interfaces of a layer is much more complicated than that of the single-interface case. First, complex wave patterns are generated and then reverberate between the two interfaces as an incident shock that refracts successively on the first and second surfaces, which considerably affects the pressure distribution and vorticity deposition (Henry de Frahan, Movahed & Johnsen 2015). Secondly, the BP and RT effects may behave differently for the inner and outer interfaces with distinct radial trajectories (Ding et al.…”