Numerical Simulation of Rarefied Flow Instabilities Using Kinetic Approach

The results of numerical investigations of hydrodynamic instabilities in rarefied flows obtained using the kinetic approach are presented and discussed. The rarefied flow instabilities are simulated using both statistical and deterministic methods to solve kinetic equations for the velocity distribution function. The Direct Simulation Monte Carlo method is employed for statistical modeling of rarefied flows while the deterministic methods used are high-order finite-difference schemes for solving the Boltzmann transport equation and model kinetic equations in a multidimensional phase space. Numerical solvers used for the simulations are run on multiple-GPU clusters using CUDA platform and MPI communication interface. The development of instabilities in compressible free shear flows such as a mixing layer between two parallel streams and a plane jet in a coflow is considered. The Rayleigh–Taylor and Richtmyer–Meshkov instabilities induced by external body forces are also simulated. The results of kinetic simulations are compared with data from the linear stability theory and Navier–Stokes computations and it is shown that good agreement is observed between kinetic and continuum approaches.