Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities.

In the present work, the two-equation k-L model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)] is extended by the addition of a third equation for the mass-flux velocity. A set of model constants is derived to satisfy an ansatz of self-similarity in the low Atwood number limit. The model is then applied to the simulation of canonical Rayleigh-Taylor and Richtmyer-Meshkov test problems in one dimension and is demonstrated to reproduce analytical self-similar growth and to recover growth rates used to constrain the model.