Coupled discrete unified gas kinetic scheme for the thermal compressible flows in all Knudsen number regimes

Liu, Hongtao; Kong, Mingchi; Chen, Qing; Zheng, Liang; Cao, Yong

doi:10.1103/physreve.98.053310

Cited by 23 publications

(6 citation statements)

References 46 publications

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“…The total energy double-distribution-function model (TEDDF) is originally proposed by Guo et al [11] and then generalized by Liu et al [34] to simulate thermal compressible flows. The TEDDF model is briefly introduced as follows.…”

Section: The Total Energy Double-distribution-function Modelmentioning

confidence: 99%

Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis

et al. 2021

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In this paper, based on simplified Boltzmann equation, we explore the inverse-design of mesoscopic models for compressible flow using the Chapman-Enskog analysis. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the NSF system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored using the DNS simulation data based on the proposed model.

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Section: The Total Energy Double-distribution-function Modelmentioning

confidence: 99%

Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis

et al. 2021

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“…The von Neumann scheme increases the numerical scaling of the problem to O(N 2n log N ). However, there has been some interest in the solvers with similar scaling [39][40][41], and in some cases where a continuous (as opposed to discretely sampled with sheets) velocity dispersion is necessary to recover the correct solution this solver may be preferable.…”

Section: Von Neumann-poisson Solvermentioning

confidence: 99%

Investigating the use of field solvers for simulating classical systems

et al. 2020

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We explore the use of field solvers as approximations of classical Vlasov-Poisson systems. This correspondence is investigated in both electrostatic and gravitational contexts. We demonstrate the ability of field solvers to be excellent approximations of problems with cold initial condition into the nonlinear regime. We also investigate extensions of the Schrödinger-Poisson system that employ multiple stacked cold streams, and the von Neumann-Poisson equation as methods that can successfully reproduce the classical evolution of warm initial conditions. We then discuss how appropriate simulation parameters need to be chosen to avoid interference terms, aliasing, and wave behavior in the field solver solutions. We present a series of criteria clarifying how parameters need to be chosen in order to effectively approximate classical solutions.

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“…The total energy double-distribution-function model (TEDDF) is originally proposed by Guo et al [8] and then generalized by Liu et al [26] to simulate thermal compressible flows. The TEDDF model is briefly introduced as follows.…”

Section: The Total Energy Double-distribution-function Modelmentioning

confidence: 99%

A general framework for the inverse design of mesoscopic models based on the Boltzmann equation

Chen¹,

Wang²,

Lai³

et al. 2020

Preprint

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In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored under this framework.

show abstract

Coupled discrete unified gas kinetic scheme for the thermal compressible flows in all Knudsen number regimes

Cited by 23 publications

References 46 publications

Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis

Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis

Investigating the use of field solvers for simulating classical systems

A general framework for the inverse design of mesoscopic models based on the Boltzmann equation

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