On the Richtmyer-Meshkov instability evolving from a deterministic multimode planar interface

Abstract: We investigate the shock-induced turbulent mixing between a light and heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a $\Ma = 1.5$ shock wave. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Well-resolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies the focus of the present investigation is to quantify uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and non-linear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependencies on the small-scale flow field structures in consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive.