Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models

Qi，Yiming1; Wang，Lian Ping2; Guo，Zhaoli3; Chen，Shiyi1,2,4

2023-12-01

10.1103/PhysRevE.108.065301

Physical Review E   影响因子和分区

2470-0045

2470-0053

A lifting relation connecting the distribution function explicitly with the hydrodynamic variables is necessary for the Boltzmann equation-based mesoscopic approaches in order to correctly initialize a nonuniform hydrodynamic flow. We derive two lifting relations for Guo et al.'s total-energy double-distribution-function (DDF) kinetic model [Z. L. Guo et al., Phys. Rev. E 75, 036704 (2007)1539-375510.1103/PhysRevE.75.036704], one from the Hermite expansion of the conserved and nonconserved moments, and the second from the O(τ) Chapman-Enskog (CE) approximation of the Maxwellian exponential equilibrium. While both forms are consistent to the compressible Navier-Stokes-Fourier system theoretically, we stress that the latter may introduce numerical oscillations under the recently optimized discrete velocity models [Y. M. Qi et al., Phys. Fluids 34, 116101 (2022)10.1063/5.0120490], namely a 27 discrete velocity model of the seventh-order Gauss-Hermite quadrature (GHQ) accuracy (D3V27A7) for the velocity field combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5) for the total energy. It is shown that the Hermite-expansion-based lifting relation can be alternatively derived from the latter approach using the truncated Hermite-polynomial equilibrium. Additionally, a relationship between the order of CE expansions and the truncated order of Hermite equilibria is developed to determine the minimal order of a Hermite equilibria required to recover any multiple-timescale macroscopic system. Next, three-dimensional compressible Taylor-Green vortex flows with different initial conditions and Ma numbers are simulated to demonstrate the effectiveness and potential issues of these lifting relations. The Hermite-expansion-based lifting relation works well in all cases, while the Chapman-Enskog-expansion-based lifting relation may produce numerical oscillations and a theoretical model is developed to predict such oscillations. Furthermore, the corresponding lifting relations for Qi et al.'s total energy DDF model [Y. M. Qi et al., Phys. Fluids 34, 116101 (2022)10.1063/5.0120490] are derived, and additional simulations are performed to illustrate the generality of our approach.

EI

英语

其他

20235015192555

Boltzmann equation ; Expansion ; Hydrodynamics ; Kinetic parameters ; Kinetic theory ; Navier Stokes equations ; Polynomials ; Vortex flow

Fluid Flow, General:631.1 ; Algebra:921.1 ; Calculus:921.2 ; Statistical Methods:922 ; Probability Theory:922.1 ; Classical Physics; Quantum Theory; Relativity:931 ; Materials Science:951

PHYSICS

2-s2.0-85179001171

Scopus

1.State Key Laboratory for Turbulence and Complex Systems,College of Engineering,Peking University,Beijing,100871,China
2.Guangdong Provincial Key Laboratory of Turbulence Research and Applications,Center for Complex Flows and Soft Matter Research,Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
3.Institute of Interdisciplinary Research for Mathematics and Applied Science,Huazhong University of Science and Technology,Wuhan,Hubei,430074,China
4.Eastern Institute for Advanced Study,Eastern Institute of Technology,Ningbo,Zhejiang,315200,China

Qi，Yiming,Wang，Lian Ping,Guo，Zhaoli,et al. Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models[J]. Physical Review E,2023,108(6).

Qi，Yiming,Wang，Lian Ping,Guo，Zhaoli,&Chen，Shiyi.(2023).Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models.Physical Review E,108(6).

Qi，Yiming,et al."Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models".Physical Review E 108.6(2023).