The k-L turbulence model, where k is the turbulent kinetic energy and L represents the turbulent eddy scale length, is a two-equation turbulence model that has been proposed to simulate turbulence induced by Rayleigh-Taylor (RT) and Richtmyer Meshkov (RM) instabilities, which play an important role in the implosions of inertial confinement fusion (ICF) capsule targets. There are three free parameters in the k-L model, and in this paper, I calibrate them independently by comparing with RT and RM data from the linear electric motor (LEM) experiments together with classical Kelvin-Helmoholtz (KH) data. To perform this calibration, I numerically solved the equations of one-dimensional (1D) Lagrangian hydrodynamics, in a manner similar to that of contemporary ICF codes, together with the k-L turbulence model. With the three free parameters determined, I show that the k-L model is successful in describing both shear-driven and buoyancy-driven instabilities, capturing the experimentally observed separation between bubbles and spikes at high Atwood number for the RT case, as well as the temporal mix width recorded in RM shock tube experiments.

A 3D verification and validation suite of test problems is presented and used to evaluate hydrodynamic methods within a radiation hydrodynamics code, xRAGE. These test problems exercise different levels of complexity, building towards ICF problems which in addition to hydrodynamics also include three temperature plasma physics, thermal conduction, and radiation diffusion. Among the problems in the test suite are the Kidder ball problem, the Verney shell problem, and a 5-material compression problem, which exercise different purely hydrodynamic methods implemented within xRAGE. There is excellent agreement between 2D and 3D XRAGE simulation results and between the xRAGE results and the benchmark solutions. Two 3D ICF test problems are also presented, based on an OMEGA direct drive capsule experiment and on a NIF indirect drive capsule experiment. It is demonstrated that the newer unsplit hydrodynamic method in xRAGE produces more vorticity relative to the older default method. For the indirect drive capsule, the 3D simulations are in reasonable agreement with the experimental values of ion temperature and neutron production.