Simulation of fluid mixing in acceleration driven instabilities

Abstract

This chapter presents a numerical study of two fluid interface instabilities, the gravity-driven Rayleigh-Taylor (RT) instability, and the shock-driven Richtmyer-Meshkov (RM) instability, using the front tracking method. It compares the numerical solutions with tracked and untracked algorithms and explains the quantitative difference of the acceleration rate in the RT instability. The chapter also compares the difference of the numerical solutions with conservative and nonconservative tracking algorithms in the RM instability along with the study on the growth rate of RT mixing through a high-resolution front-tracking method. Earlier front-tracking simulations of multimode RT instability achieved bubble envelope growth rates, ɑ, in agreement with experiment. The chapter also presents a theory that is well supported by diagnostics, explaining the main cause for the discrepancy between bubble growth rates obtained by experiments and those of diffusive simulations. The compressible fluids in the RT and RM instabilities are modeled by the Euler equations for conservation of mass, momentum, and energy. This system of nonlinear hyperbolic equations allows discontinuous solutions, such as contact surfaces and shocks.