A conserved discrete unified gas kinetic scheme for microchannel gas flows in all flow regimes

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

doi:10.1016/j.compfluid.2018.03.023

Cited by 45 publications

(19 citation statements)

References 57 publications

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“…Combining the advantages of the lattice Boltzmann method (LBM) [32] and the unified gas kinetic scheme (UGKS) [15], the DUGKS [31] was proposed recently for rarefied gas flows, which is applicable to the entire flow regimes. It has been successfully applied to low-speed isothermal flows ranging from the continuum to free molecular flow regimes [31], compressible flows considering heat transfer and shock discontinuity [33], flows of binary gas mixtures [14], Boussinesq flows [34], multiscale heat transfer [35][36][37], thermally induced non-equilibrium flows [38], rarefied gas flow in micro-channels [39], solid-liquid phase change problems [40], immiscible two phase flows [41] etc.. The capability of the DUGKS to tackle multiscale problems has been thoroughly discussed in these studies, and a rigorous theoretical analysis of its unified preserving properties was also made recently [42].…”

Section: Introductionmentioning

confidence: 99%

Discrete unified gas kinetic scheme for all Knudsen number flows. IV. Strongly inhomogeneous fluids

et al. 2020

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This work is an extension of the discrete unified gas kinetic scheme (DUGKS) from rarefied gas dynamics to strongly inhomogeneous dense fluid systems. The fluid molecular size can be ignored for dilute gases, while the nonlocal intermolecular collisions and the competition of solid-fluid and fluid-fluid interactions play an important role for surface-confined fluid flows at the nanometer scale. The non-equilibrium state induces strong fluid structural inhomogeneity and anomalous fluid flow dynamics. According to the previous kinetic model [Z. L. Guo et al., Phy. Rev. E 71, 035301 (2005)], the long-range intermolecular attraction is modeled by the mean-field approximation, and the volume exclusion effect is considered by hard-sphere potential in the collision operator. The kinetic model is solved by the DUGKS, which has the characteristics of asymptotic preserving, low dissipation, second order accuracy and multidimensional nature. Both static fluid structure and dynamic flow behaviors are calculated and validated with Monte Carlo or molecular dynamics results. It is shown that the flow of dense fluid systems tends to that of rarefied gases as the dense degree decreases or the mean flow path increases. The DUGKS is proved to be applicable to simulate such non-equilibrium dense fluid systems.

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Section: Introductionmentioning

confidence: 99%

Discrete unified gas kinetic scheme for all Knudsen number flows. IV. Strongly inhomogeneous fluids

et al. 2020

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“…This approach was also adopted in some later conserved DUGKS methods [49,50]. An advantage of this approach is that macroscopic conservation (in terms of W ) from the discrete collision term is satisfied exactly, regardless of the quadrature rule for the integral in velocity space.…”

Section: Formulationmentioning

confidence: 99%

Progress of discrete unified gas-kinetic scheme for multiscale flows

Guo

2021

Adv. Aerodyn.

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Multiscale gas flows appear in many fields and have received particular attention in recent years. It is challenging to model and simulate such processes due to the large span of temporal and spatial scales. The discrete unified gas kinetic scheme (DUGKS) is a recently developed numerical approach for simulating multiscale flows based on kinetic models. The finite-volume DUGKS differs from the classical kinetic methods in the modeling of gas evolution and the reconstruction of interface flux. Particularly, the distribution function at a cell interface is reconstructed from the characteristic solution of the kinetic equation in space and time, such that the particle transport and collision effects are coupled, accumulated, and evaluated in a numerical time step scale. Consequently, the cell size and time step of DUGKS are not passively limited by the particle mean-free-path and relaxation time. As a result, the DUGKS can capture the flow behaviors in all regimes without resolving the kinetic scale. Particularly, with the variation of the ratio between numerical mesh size scale and kinetic mean free path scale, the DUGKS can serve as a self-adaptive multiscale method. The DUGKS has been successfully applied to a number of flow problems with multiple flow regimes. This paper presents a brief review of the progress of this method.

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“…Recently, Liu et al proposed a conserved-DUGKS (C-DUGKS) for isothermal micro-channel flows in all flow regimes [22]. Like the original DUGKS, the C-DUGKS also calculates the micro-flux at the cell interface by means of the characteristic-line theory using the auxiliary distribution functions, while the discrete distribution functions and macroscopic conservative variables (mass, momentum and energy) are updated simultaneously to ensure the conservation of numerical collision term in a time implicitly form which is similar to that of the UGKS method.…”

Section: Introductionmentioning

confidence: 99%

Conserved discrete unified gas-kinetic scheme with unstructured discrete velocity space

et al. 2019

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Discrete unified gas-kinetic scheme (DUGKS) is a multi-scale numerical method for flows from continuum limit to free molecular limit, and is especially suitable for the simulation of multi-scale flows, benefiting from its multi-scale property. To reduce integration error of the DUGKS and ensure the conservation property of the collision term in isothermal flow simulations, a Conserved-DUGKS (C-DUGKS) is proposed. On the other hand, both DUGKS and C-DUGKS adopt Cartesian-type discrete velocity space, in which Gaussian and Newton-Cotes numerical quadrature are used for calculating the macroscopic physical variables in low speed and high speed flows, respectively. While, the Cartesian-type discrete velocity space leads to huge computational cost and memory demand. In this paper, the isothermal C-DUGKS is extended to the non-isothermal case by adopting coupled mass and inertial energy distribution functions. Moreover, since the unstructured mesh, such as the triangular mesh in two dimensional case, is more flexible than the structured Cartesian mesh, it is introduced to the discrete velocity space of C-DUGKS, such that more discrete velocity points can be arranged in the velocity regions that enclose large number of molecules, and only a few discrete velocity points need to be arranged in the velocity regions with small amount of molecules in it. By using the unstructured discrete velocity space, the computational efficiency of C-DUGKS is significantly increased. A series of numerical tests in a wide range of Knudsen numbers, such as the Couette flow, lid-driven cavity flow, two-dimensional rarefied Riemann problem and the supersonic cylinder flows, are carried out to examine the validity and efficiency of the present method.

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A conserved discrete unified gas kinetic scheme for microchannel gas flows in all flow regimes

Cited by 45 publications

References 57 publications

Discrete unified gas kinetic scheme for all Knudsen number flows. IV. Strongly inhomogeneous fluids

Discrete unified gas kinetic scheme for all Knudsen number flows. IV. Strongly inhomogeneous fluids

Progress of discrete unified gas-kinetic scheme for multiscale flows

Conserved discrete unified gas-kinetic scheme with unstructured discrete velocity space

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