The continuum medium hypothesis in the rarefied non-equilibrium flow field has been invalid, and the rarefied non-equilibrium flow is mainly researched around the Boltzmann equation with the Unified Gas-Kinetic Scheme (UGKS) as a representative method. In numerical simulation of the rarefied non-equilibrium flow, the Navier-Stokes (N-S) equation has high efficiency but low accuracy while the UGKS method has high accuracy but low efficiency. In this paper, a Data-driven method for the solution of the Nonlinear Constitutive Relations of the rarefied non-equilibrium flow based on the N-S equation and the UGKS method (DNCR) is proposed. The flow field numerical simulation results of the N-S solver and the UGKS solver are used as the data set. Based on the characteristic parameters of the flow field, an extremely randomized trees algorithm is adopted to nonlinearly correct the linear viscous stress term and heat flux term of the N-S equation. The numerical solution of the rarefied non-equilibrium flow is obtained by solving the N-S macro-conservation equation via coupling nonlinear constitutive relations. A two-dimensional lid-driven cavity case is used to select and tune the characteristic parameters involved in high-dimensional non-linear modeling. Several typical states are selected for the study of the generalization ability of the extremely randomized trees model. Finally, the evaluation of calculation accuracy and efficiency shows the superiority of the method proposed in this paper.
LI Tingwei
,
ZHANG Mang
,
ZHAO Wenwen
,
CHEN Weifang
,
JIANG Lijian
. Machine learning method for correction of rarefied nonlinear constitutive relations[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021
, 42(4)
: 524386
-524386
.
DOI: 10.7527/S1000-6893.2020.24386
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