An efficient statistical noise-free kinetic method for collisional rarified gas simulations

A new grid method for the gas modeling in weakly-to-moderately collisional regimes is proposed. The procedure could be qualified as an operator-splitting scheme with analytical sub-steps. The latter utilize either exact or quasi-analytical solutions of the fractional sub-steps for the spatial transport and collisional terms. The detailed consideration is given to a BGK term, though generalization to a Boltzmann collisional operator is possible. Proof of the full - mass, momentum, and energy - conservation is given. Higher order schemes are discussed as well. Efficiency and accuracy are demonstrated on the two classical problems: shear wave damping and back-step flow. Results from the 2D2V simulations of the actual engineering systems are presented.