Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

Spurious currents near an interface between different phases are a common undesirable feature of the lattice Boltzmann equation (LBE) method for two-phase systems. In this paper, we show that the spurious currents of a kinetic theory-based LBE have a significant dependence on the parity of the grid number of the underlying lattice, which can be attributed to the chequerboard effect. A technique that uses a Lax–Wendroff streaming is proposed to overcome this anomaly, and its performance is verified numerically.

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Kinetic theory-based force analysis in lattice Boltzmann equation

International Journal of Modern Physics C ◽

10.1142/s0129183119500220 ◽

2019 ◽

Vol 30 (04) ◽

pp. 1950022

Author(s):

Lin Zheng ◽

Song Zheng ◽

Qinglan Zhai

Keyword(s):

Distribution Function ◽

Boltzmann Equation ◽

Kinetic Theory ◽

Density Distribution ◽

Lattice Boltzmann ◽

Local Equilibrium ◽

Equilibrium Density ◽

Lattice Boltzmann Equation ◽

Force Term ◽

Density Distribution Function

In the gas kinetic theory, it is shown that the zeroth order of the density distribution function [Formula: see text] and local equilibrium density distribution function were the Maxwellian distribution [Formula: see text] with an external force term, where [Formula: see text] is the fluid density, [Formula: see text] is the physical velocity and [Formula: see text] is the temperature, while in the lattice Boltzmann equation (LBE) method, numerous force treatments were proposed with a discrete density distribution function [Formula: see text] apparently relaxed to a given state [Formula: see text], where the given velocity [Formula: see text] could be different with [Formula: see text], and the Chapman–Enskog (CE) analysis showed that [Formula: see text] and local equilibrium density distribution function should be [Formula: see text] in the literature. In this paper, we start from the kinetic theory and show that the [Formula: see text] and local equilibrium density distribution function in LBE should obey the Maxwellian distribution [Formula: see text] with [Formula: see text] relaxed to [Formula: see text], which are consistent with kinetic theory. Then the general requirements for the force term are derived, by which the correct hydrodynamic equations could be recovered at Navier–Stokes (NS) level, and numerical results confirm our theoretical analysis.

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Lattice Boltzmann equation for axisymmetric thermal flows

Computers & Fluids ◽

10.1016/j.compfluid.2010.01.006 ◽

2010 ◽

Vol 39 (6) ◽

pp. 945-952 ◽

Cited By ~ 34

Author(s):

Lin Zheng ◽

Baochang Shi ◽

Zhaoli Guo ◽

Chuguang Zheng

Keyword(s):

Boltzmann Equation ◽

Lattice Boltzmann ◽

Lattice Boltzmann Equation ◽

Thermal Flows

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Coda

10.1093/oso/9780199592357.003.0036 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Fluid Dynamics ◽

Boltzmann Equation ◽

Broad Spectrum ◽

Lattice Boltzmann ◽

Lattice Boltzmann Equation ◽

Real Difference ◽

Complex Flow ◽

Flow Problems ◽

Subjective View

This section of the book revisits a question from the book The Lattice Boltzmann Equation (for fluid dynamics and beyond). This question is: What did we learn through lattice Boltzmann? Did LB make a real difference to our understanding of the physics of fluids and flowing matter in general? Here, the text aims to offer a subjective view, without the presumption of being right. Besides being routinely used for a broad spectrum of complex flow problems, there are, in the opinion expressed in this part of the book, a few precious instances in which LB has made a palpable difference.

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