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 accuracy of both ES-FP equation and FP-DVM method are examined using a series of 0D-3V homogenous relaxation cases and 1D-3V shock structure cases with different M ach numbers, in which 1D-3V cases are reduced to 1D-quasi 1V cases. Both the predictions of 0D-3V and 1D-3V cases match well with the benchmark results such as analytical Boltzmann solution, direct full-Boltzmann numerical solution and DSMC result. Especially, the FP-DVM predictions match well with the DSMC results in the M ach 8.0 shock structure case, which is in high non-equilibrium, and is a challenge case of the model Boltzmann equation and the corresponding numerical methods.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.