Modeling fluid instabilities in inertial confinement fusion hydrodynamics codes

The numerical tools typically used to model the evolution of fluid instabilities in inertial confinement fusion hydrodynamics codes are examined, and some are found to have properties which would seem to be incompatible with the accurate modeling of small-amplitude perturbations, i.e., perturbations in the linear stage of evolution. In particular a “differentiability condition” which is satisfied by the physics in such situations is not necessarily satisfied by the numerical algorithms in typical use. It is demonstrated that it is possible to remove much of the nondifferentiability in many cases, and that substantial improvement in one’s ability to accurately model the evolution of small-amplitude perturbations can result. First a simple example involving a nondifferentiable radiation transport algorithm is shown, and then the nondifferentiabilities introduced by the use of upwind and “high resolution” hydrodynamics algorithms are analyzed.