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A conservative discrete velocity method for the ellipsoidal Fokker-Planck equation in gas-kinetic theory by Liu, Sha; Yuan, Ruifeng; Javid, Usman; Zhong, Chengwen is a scholarly article available to read on EtoBox.

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A conservative discrete velocity method (DVM) is developed for the ellipsoidal Fokker-Planck (ES-FP) equation in prediction of non-equilibrium neutral gas flows in this paper. The ES-FP collision operator is solved in discrete velocity space in a concise and quick finite difference framework. The conservation problem of discrete ES-FP collision operator is solved by multiplying each term in it by extra conservative coefficients whose values are very closed to unity. Their differences to unity are in the same order of the numerical error in approximating the ES-FP operator in discrete velocity space. All the macroscopic conservative variables (mass, momentum and energy) are conserved in the present modified discrete ES-FP collision operator. Since the conservation property in discrete element of physical space is very important for numerical scheme when discontinuity and large gradient exist in flow field, a finite volume framework is adopted for the transport term of ES-FP equation. For $nD$-$3V$ ($n<3$) cases, a $nD$-quasi $nV$ reduction is specially proposed for ES-FP equation and the corresponding FP-DVM method, which can greatly reduce the computational cost. The validity and a

Author

Liu, Sha; Yuan, Ruifeng; Javid, Usman; Zhong, Chengwen

Published

2019

Language

EN