On symbolic derivation of the cumulant equations

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• 作者：Seeger ; Steffen ; Hoffmann ; Karl Heinz
• 关键词：Boltzmann equation ; Moment method ; Cumulant method ; Mathematica ; Symbolic calculation
• 刊名：Computer Physics Communications
• 出版年：2005
• 出版时间：June 15, 2005
• 年：2005
• 卷：168
• 期：3
• 页码：165-176
• 全文大小：160 K

文摘

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.