The cumulant method for computational kinetic theory

We propose a new method for numerical simulation of gas dynamics based on k inetic theory. The method is based on a cumulant-expansion-ansatz for the p hase space density, which leads to a set of quasi-linear, hyperbolic partia l differential equations. The method is compared to the moment method of Gr ad. Both methods agree for low-order approximations but the method proposed shows additional non-linear terms for high order approximations. Boundary conditions on the cumulants for an ideally reflecting and an ideally rough boundary surface are derived from conditions on the phase space density. A LAX-method is used for numerical analysis of a 2d-BGK fluid, which results in an easy-to-implement algorithm well suited for implementation on massivl y parallel computers. The results are found to agree qualitatively with pre dictions from moment theories.