Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters

Sofonea, Victor

doi:10.1016/j.jcp.2009.05.009

Cited by 25 publications

(23 citation statements)

References 56 publications

(97 reference statements)

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“…As some discontinuities may occur at wall surface in the following simulations, we will employ the forward Euler method for time discretization and the second-order total variation diminishing (TVD) scheme for space discretization along the grid (see Fig.2) for Eq. (16) [28,52,53,54]. According to the characteristics of problems, one can also choose any other appropriate numerical method to solve Eq.…”

Section: Numerical Schemementioning

confidence: 99%

Multiscale lattice Boltzmann approach to modeling gas flows

Meng

Zhang

Shan³

2011

Phys. Rev. E

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For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different theoretical frameworks. In particular, it is not easy to recover the non-equilibrium information required by the kinetic method which is lost by the continuum model at the coupling interface. Therefore, we present a multiscale lattice Boltzmann (LB) method which deploys high-order LB models in highly rarefied flow regions and low-order ones in less rarefied regions. Since this multiscale approach is based on the same theoretical framework, the coupling precess becomes simple. The non-equilibrium information will not be lost at the interface as low-order LB models can also retain this information. The simulation results confirm that the present method can achieve model accuracy with reduced computational cost.

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Section: Numerical Schemementioning

confidence: 99%

Multiscale lattice Boltzmann approach to modeling gas flows

Meng

Zhang

Shan³

2011

Phys. Rev. E

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“…Therefore, high-order contributions f (n) α (n ≥ 1) of the CE expansion do not contribute to the macroscopic density and flow velocity. By inserting the CE ansatz (28) and (29) into the Boltzmann equation (27) we find the general solution for n ≥ 1…”

Section: A Chapman-enskog Analysismentioning

confidence: 99%

High-order lattice Boltzmann models for wall-bounded flows at finite Knudsen numbers

Feuchter

2016

Phys. Rev. E

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We analyze a large number of high-order discrete velocity models for solving the Boltzmann-BGK equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved flow regimes for low Mach numbers. Although high-order lattice Boltzmann models recover flow regimes beyond the Navier-Stokes level we observe for several models significant deviations from reference results. We found this to be caused by their inability to recover the Maxwell boundary condition exactly. By using supplementary conditions for the gas-surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse Maxwell boundary condition accurately. Both high-order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results. For Poiseuille flow, we can reproduce the mass flow and slip velocity up to the Knudsen number of 1. Moreover, for small Knudsen numbers, the Knudsen layer behavior is recovered.

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“…However, due to the multi-speed lattice of high-order models, the formulation of the kinetic diffuse-reflection boundary condition with the characteristic "streaming and collision" mechanism is yet to be developed. The successful implementations so far for high-order models are based on various finite difference scheme [7,8], where the highly desirable "streaming and collision" mechanism disappears. Because of this "streaming and collision" mechanism, LB method is often regarded a particle method.…”

Section: Introductionmentioning

confidence: 99%