On symbolic derivation of the cumulant equations Original Research Article

We discuss the application of Mathematica for automated, symbolic calculation of the cumulant equations of arbitrary order. Like moment equations, these partial differential equations—describing fluid motion on a mesoscopic scale—may be considered an approximation to the Boltzmann equation, a highly nonlinear integro-differential equation that describes the motion of gases at a microscopic scale. Though the cumulant method provides a simple and compact presentation of the theory, actual calculation of very high order equations turns out to be a challenging task.