Double distribution function-based discrete gas kinetic scheme for viscous incompressible and compressible flows

Zhang, Liangqi; Жен, Чен; Yang, Liming; Chen, Shu

doi:10.1016/j.jcp.2020.109428

Cited by 6 publications

(1 citation statement)

References 54 publications

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“…In present work, a kinetic flux reconstruction strategy is introduced in modeling flow evolution. Macroscopic flux is applied to flow evolution for improving macroscopic conservation [28]. Gas distribution function at next time step is applied to reconstruct particle motion in a mesh cell [29].…”

Section: Introductionmentioning

confidence: 99%

A simplified discrete unified gas kinetic scheme for incompressible flow

Zhong

Zou

Pan

et al. 2020

Preprint

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The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows which combines the benefits of both Lattice Boltzmann Method (LBM) and unified gas kinetic scheme (UGKS). By reconstruction of gas distribution function using particle velocity characteristic line, flux contains more detailed information of fluid flow and more concrete physical nature. In this work, a simplified DUGKS is proposed with reconstruction stage on a whole time step instead of half time step in original DUGKS. Using temporal/spatial integral Boltzmann Bhatnagar-Gross-Krook (BGK) equation, the transformed distribution function with inclusion of collision effect is constructed. The macro and mesoscopic fluxes of the cell on next time step is predicted by reconstruction of transformed distribution function at interfaces along particle velocity characteristic lines. According to the conservation law, the macroscopic variables of the cell on next time step can be updated through its macroscopic flux. Equilibrium distribution function on next time step can also be updated. Gas distribution function is updated by FV scheme through its predicted mesoscopic flux in a time step. Compared with the original DUGKS, the computational process of the proposed method is more concise because of the omission of half time step flux calculation. Numerical time step is only limited by the Courant-Friedrichs-Lewy (CFL) condition and relatively good stability has been preserved. Several test cases, including the Couette flow, lid-driven cavity flow, laminar flows over a flat plate, a circular cylinder, and an airfoil, as well as micro cavity flow cases are conducted to validate present scheme. The numerical simulation results agree well with the references' results.

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Section: Introductionmentioning

confidence: 99%

A simplified discrete unified gas kinetic scheme for incompressible flow

Zhong

Zou

Pan

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

A simplified discrete unified gas kinetic scheme for incompressible flow

et al. 2020

View full text Add to dashboard Cite

The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows, which combines the benefits of both the lattice Boltzmann method and UGKS. By the reconstruction of the gas distribution function using particle velocity characteristic lines, the flux contains more detailed information of fluid flow and more concrete physical nature. In this work, a simplified DUGKS is proposed with the reconstruction stage on a whole time step instead of a half time step in the original DUGKS. Using the temporal/spatial integral Boltzmann Bhatnagar–Gross–Krook equation, the auxiliary distribution function with the inclusion of the collision effect is adopted. The macroscopic and mesoscopic fluxes of the cell on the next time step are predicted by the reconstruction of the auxiliary distribution function at interfaces along particle velocity characteristic lines. According to the conservation law, the macroscopic variables of the cell on the next time step can be updated through its flux, which is a moment of the predicted mesoscopic flux at cell interfaces. The equilibrium distribution function on the next time step can also be updated. The gas distribution function is updated by the FV scheme through its predicted mesoscopic flux in a time step. Compared with the original DUGKS, the computational process of the proposed method is more concise because of the omission of half time step flux calculation. The numerical time step is only limited by the Courant–Friedrichs–Lewy condition, and a relatively good stability has been preserved. Several test cases, including the Couette flow, lid-driven cavity flow, laminar flows over a flat plate, a circular cylinder, and an airfoil, and microcavity flow cases, are conducted to validate the present scheme. The observed numerical simulation results reasonably agree with the reported results.

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Toward fully conservative hybrid lattice Boltzmann methods for compressible flows

et al. 2020

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This article presents a new numerical scheme designed to solve for any scalar equation coupled with a Lattice-Boltzmann solver (in so-called hybrid methods). Its most direct application is to solve an energy equation, in parallel with a Lattice-Boltzmann solver dealing with mass and momentum conservation.The numerical scheme is specifically designed to compute the energy flux consistently with the mass and momentum flux (as is done, for instance, using Riemann solvers).This scheme effectively lifts a major limitation of current compressible hybrid Lattice-Boltzmann, in which the energy conservation is tackled under nonconservative form, leading to discretization errors on jump conditions across shocks.Combined with our recently presented pressure-based solver [G. Farag et al, Physics of Fluids, vol. 32, no. 6, p. 066106, (2020)], the resulting hybrid Lattice-Boltzmann scheme is, to the authors' knowledge, the first to numerically conserve simultaneously mass, momentum and total energy.

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Double distribution function-based discrete gas kinetic scheme for viscous incompressible and compressible flows

Cited by 6 publications

References 54 publications

A simplified discrete unified gas kinetic scheme for incompressible flow

A simplified discrete unified gas kinetic scheme for incompressible flow

A simplified discrete unified gas kinetic scheme for incompressible flow

Toward fully conservative hybrid lattice Boltzmann methods for compressible flows

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