Numerical Experiments with a Turbulent Single-Mode Rayleigh-Taylor Instability

Abstract

Direct numerical simulation is a powerful tool for studying turbulent flows. Unfortunately, it is also computationally expensive and often beyond the reach of the largest, fastest computers. Consequently, a variety of turbulence models have been devised to allow tractable and affordable simulations of averaged flow fields. Unfortunately, these present a variety of practical difficulties, including the incorporation of varying degrees of empiricism and phenomenology, which leads to a lack of universality. This unsatisfactory state of affairs has led to the speculation that one can avoid the expense and bother of using a turbulence model by relying on the grid and numerical diffusion of the computational fluid dynamics algorithm to introduce a spectral cutoff on the flow field and to provide dissipation at the grid scale, thereby mimicking two main effects of a large eddy simulation model. This paper shows numerical examples of a single-mode Rayleigh-Taylor instability in which this procedure produces questionable results. We then show a dramatic improvement when two simple subgrid-scale models are employed. This study also illustrates the extreme sensitivity to initial conditions that is a common feature of turbulent flows.

Numerical Experiments Using a Convective Flux Limiter on a Turbulent Single-Mode Rayleigh-Taylor Instability

“…Perhaps it is the strong cross-stream diffusion along the sides of the spike. In any case, we have seen that resolution improves this situation [15].…”

“…As discussed in a previous report, this solution has very poor accuracy [15]. Not only is the shape of the interface all wrong, the dispersive errors are enormous.…”

“…In all cases, the 7.3 by 8.8 em mesh was covered by a uniform grid of 73 x 88 zones. The initial and boundary conditions were the same as in a previous study [15]. in the zi direction [8].…”

“…The accuracy can be improved by increased resolution, but even zones 0.25 as wide still have unacceptable errors and show a lack of grid independence. [15]. Notice also that the time step has dropped from 25 #s down to a little over 4 ps due to the need to resolve the fine-scale numerical artifacts.…”