Appearance of deterministic mixing behavior from ensembles of fluctuating hydrodynamics simulations of the Richtmyer-Meshkov instability

Physical Review. E
Kiran Narayanan, Ravi Samtaney

Abstract

We obtain numerical solutions of the two-fluid fluctuating compressible Navier-Stokes (FCNS) equations, which consistently account for thermal fluctuations from meso- to macroscales, in order to study the effect of such fluctuations on the mixing behavior in the Richtmyer-Meshkov instability (RMI). The numerical method used was successfully verified in two stages: for the deterministic fluxes by comparison against air-SF_{6} RMI experiment, and for the stochastic terms by comparison against the direct simulation Monte Carlo results for He-Ar RMI. We present results from fluctuating hydrodynamic RMI simulations for three He-Ar systems having length scales with decreasing order of magnitude that span from macroscopic to mesoscopic, with different levels of thermal fluctuations characterized by a nondimensional Boltzmann number (Bo). For a multidimensional FCNS system on a regular Cartesian grid, when using a discretization of a space-time stochastic flux Z(x,t) of the form Z(x,t)→1/sqrt[h▵t]N(ih,nΔt) for spatial interval h, time interval Δt, h, and Gaussian noise N should be greater than h_{0}, with h_{0} corresponding to a cell volume that contains a sufficient number of molecules of the fluid such that the fluctuations are phys...Continue Reading

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