Single-mode bubble evolution simulations of Rayleigh Taylor instability with spectral element method and a viscous model

Based on the single-mode potential model of Jacobs and Rikanati, Firstly, a viscous single-mode bubble evolution model of Rayleigh Taylor instability (RTI) is developed in this study. Viscous effects of RTI's early stage growth for low Atwood number have been explained. In addition, direct numerical simulations of single mode RTI are studied with Navier-Stokes equations and a transport-diffusive equation for miscible fluids, in which these equations are discritized with discontinuous Galerkin (DG) spectral element method. The turbulent mixing of RTI has kinetic energy dissipation, and the dissipation rate is determined by the inertial and viscous effects. Therefore, the numerical techniques must include a dissipation mechanism for kinetic energy. For this reason, the high accurate spectral element method is employed in this study. Agreement between the theoretical model and the numerical results shows that simulations of RTI is feasible using the mathematical miscible fluid model. The results also suggest that a high order numerical method may provide the capability of simulating small scale fluctuations in turbulent flows with RTI.