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- W2935712511 abstract "A novel Unified Gas-Kinetic Scheme (UGKS) is developed for 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 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 (the framework of UGKS) 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 FP-UGKS method, which can greatly reduce the computational cost. The validity and accuracy of both ES-FP equation and FP-UGKS method are examined using a series of $0D$-$3V$ homogenous relaxation cases and $1D$-$3V$ shock structure cases with different $Mach$ 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-UGKS predictions match well with the DSMC results in the $Mach$ 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." @default.
- W2935712511 created "2019-04-25" @default.
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- W2935712511 date "2019-04-20" @default.
- W2935712511 modified "2023-10-18" @default.
- W2935712511 title "A unified gas-kinetic scheme for Ellipsoidal Fokker-Planck equation: conservative deterministic numerical method" @default.
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