Grad's distribution function for 13 moments-based moment gas kinetic solver for steady and unsteady rarefied flows: Discrete and explicit forms

Liu，W.1; Liu，Z. J.2; Zhang，Z. L.1; Teo，C. J.1; Shu，C.1

2023-05-01

10.1016/j.camwa.2023.02.006

COMPUTERS & MATHEMATICS WITH APPLICATIONS   Impact Factor & Quartile

0898-1221

1873-7668

Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the macroscopic governing equations are derived based on the moment integral of the discrete Boltzmann equation under the finite volume framework. Numerical fluxes at the cell interface related to the macroscopic variables, stress and heat flux can be reconstructed from the Boltzmann equation along the characteristic line directly. The initial distribution function is approximated by Grad's distribution function for 13 moments at the cell interface, so the explicit expression of numerical fluxes could be derived to release the present solver from the discretization and numerical integration in the molecular velocity space. The G13-MGKS with the discrete and explicit form of numerical fluxes are examined by several tests covering the steady and unsteady flows from the continuum regime to rarefied flow regimes. Numerical results indicate that the G13-MGKS could simulate continuum flows accurately and present reasonable predictions for rarefied flows at moderate Knudsen numbers. Moreover, the consumption of computations and memory demonstrates that the present framework could preserve high efficiency.

Boltzmann equation Finite volume method Moment method Rarefied flow

SCI

English

Others

Ministry of Education (MOE) of Singapore[MOE2018-T2-1-135]

Mathematics

Mathematics, Applied

WOS:000954436000001

PERGAMON-ELSEVIER SCIENCE LTD

MATHEMATICS

2-s2.0-85149299026

Scopus

1.Department of Mechanical Engineering,National University of Singapore,10 Kent Ridge Crescent,119260,Singapore
2.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Liu，W.,Liu，Z. J.,Zhang，Z. L.,et al. Grad's distribution function for 13 moments-based moment gas kinetic solver for steady and unsteady rarefied flows: Discrete and explicit forms[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2023,137:112-125.

Liu，W.,Liu，Z. J.,Zhang，Z. L.,Teo，C. J.,&Shu，C..(2023).Grad's distribution function for 13 moments-based moment gas kinetic solver for steady and unsteady rarefied flows: Discrete and explicit forms.COMPUTERS & MATHEMATICS WITH APPLICATIONS,137,112-125.

Liu，W.,et al."Grad's distribution function for 13 moments-based moment gas kinetic solver for steady and unsteady rarefied flows: Discrete and explicit forms".COMPUTERS & MATHEMATICS WITH APPLICATIONS 137(2023):112-125.