A novel gas kinetic flux solver for simulation of continuum and slip flows

Yuan, Ziming; Yang, Liming; Chen, Shu; Liu, Zijian; Liu, Wei

doi:10.1002/fld.5013

Cited by 12 publications

(1 citation statement)

References 39 publications

(73 reference statements)

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“…For the convenience of application, the temporal and spatial derivatives of g can be reformulated as the spatial derivatives of macroscopic flow variables. The final expression of NS f can be written as [52] ( )…”

Section: Adaptive Partitioning For Identification Of Cell Types and F...mentioning

confidence: 99%

Adaptive Partitioning-based Discrete Unified Gas-Kinetic Scheme for Flows in All Flow Regimes

Yang

Liang

Ding

et al. 2022

Preprint

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The discrete unified gas kinetic scheme (DUGKS) is a multiscale approach, which can be used to obtain reasonable results in all flow regimes. The key of this method is the reconstruction of numerical fluxes at the cell interface by coupling the motion of particles from their collisions, namely the use of the discrete characteristic solution to the Boltzmann-BGK equation at the cell interface to calculate numerical fluxes. But like all the discrete velocity methods (DVMs), the computational cost of DUGKS is determined by the discretization in both the physical space and the velocity space. For the continuous flow region in the computational domain, the discretization in the velocity space is unnecessary since the distribution function can be reconstructed from the Chapman-Enskog expansion directly. To improve the efficiency of DUGKS in capturing cross-scale flow physics, an adaptive partitioning-based discrete unified gas kinetic scheme (ADUGKS) is developed in this work. The ADUGKS is designed from the discrete characteristic solution to the Boltzmann-BGK equation, which contains the initial distribution function and the local equilibrium state. The initial distribution function contributes to the calculation of free streaming fluxes and the local equilibrium state contributes to the calculation of equilibrium fluxes. If the contribution of the initial distribution function is negative., the local flow field can be regarded as the continuous flow and the Navier-Stokes (N-S) equations can be used to obtain the solution directly. Otherwise, the discrete distribution functions should be updated by the Boltzmann equation to capture the rarefied effect. Given this, the computational domain is divided into the DUGKS cell and the N-S cell based on the contribution of the initial distribution function to the calculation of free streaming fluxes. In the N-S cell, the local flow field is evolved by solving the Navier-Stokes equations, while in the DUGKS cell, both the discrete velocity Boltzmann equation and the corresponding macroscopic governing equations are solved by a modified DUGKS. Since more and more cells turn into the N-S cell with the decrease of the Knudsen number, a significant acceleration can be achieved for the ADUGKS in the continuum flow regime as compared with the DUGKS.

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Section: Adaptive Partitioning For Identification Of Cell Types and F...mentioning

confidence: 99%

Adaptive Partitioning-based Discrete Unified Gas-Kinetic Scheme for Flows in All Flow Regimes

Yang

Liang

Ding

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

An implicit high-order radial basis function-based differential quadrature-finite volume method on unstructured grids to simulate incompressible flows with heat transfer

Liu

Yang

Zhang

et al. 2022

Journal of Computational Physics

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Eu's generalized hydrodynamics with its derived constitutive model: Comparison to Grad's method and linear stability analysis

et al. 2021

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Recently, the generalized hydrodynamic equations (GHE) and nonlinear coupled constitutive relation (NCCR) model have been successfully utilized for the practical application in stable numerical computations of the non-equilibrium flows. However, their stability property has never been studied theoretically, and the inherent connection with classical Grad's moment still remains unclear. In order to clarify these issues, Eu's method, including the modeling of the non-equilibrium distribution function and the cumulant expansion for collision terms, is revisited to derive the modified moment system. A comparison of Eu's moment method with existing Grad's is presented in detail from the perspectives of distribution function and closure theory. The original infinite system of Eu's distribution function is first truncated into a finite system with 13 moments. Then through our attempt of Taylor expanding the truncated distribution function, a connection between Eu's distribution and Maxwellian and Grad's is established. Subsequently, a truncated closure method is conducted to clarify the relation between Eu's moment and Grad's moment equations. Finally, linear stability analysis of GHE and NCCR model is performed in one-dimensional and multi-dimensional processes, which shows that the equations are unconditionally stable for all wavenumbers and frequencies in the equilibrium rest state (ui0=0) and uniform-moving state (ui0≠0). The linear stability of GHE and NCCR model assures their numerical stability in the multi-dimensional computations, which can be deemed as one of the major benefits of Eu's theory.

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A novel gas kinetic flux solver for simulation of continuum and slip flows

Cited by 12 publications

References 39 publications

Adaptive Partitioning-based Discrete Unified Gas-Kinetic Scheme for Flows in All Flow Regimes

Adaptive Partitioning-based Discrete Unified Gas-Kinetic Scheme for Flows in All Flow Regimes

An implicit high-order radial basis function-based differential quadrature-finite volume method on unstructured grids to simulate incompressible flows with heat transfer

Eu's generalized hydrodynamics with its derived constitutive model: Comparison to Grad's method and linear stability analysis

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