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On symbolic derivation of the cumulant equations

Steffen Seeger
Karl Heinz Hoffmann
Organization: Technische Universitat
Department: Institut fur Physik
Journal / Anthology

Computer Physics Communications
Year: 2005
Volume: 168
Issue: 3
Page range: 165-176

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.

*Mathematics > Calculus and Analysis > Differential Equations
*Science > Physics > Fluid Mechanics