Scattering kernels for the boundary conditions of the boltzmann equation on the moving boundary of two-phase systems

Meccanica ◽  
1978 ◽  
Vol 13 (3) ◽  
pp. 127-132 ◽  
Author(s):  
Nicola Bellomo ◽  
Roberto Monaco
Keyword(s):  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Moving Boundary ◽  
Two Phase ◽  
The Boltzmann Equation ◽  
Phase Systems

scholarly journals Chequerboard effects on spurious currents in the lattice Boltzmann equation for two-phase flows

2011 ◽  
Vol 369 (1944) ◽  
pp. 2283-2291 ◽  
Author(s):  
Zhaoli Guo ◽  
Baochang Shi ◽  
Chuguang Zheng
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Equation ◽  
Two Phase Flows ◽  
Two Phase ◽  
Significant Dependence ◽  
Phase Systems ◽  
Spurious Currents ◽  
Undesirable Feature

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.

The study of the Boltzmann equation of solid-gas two-phase flow with three-dimensional BGK model

2018 ◽  
Author(s):  
Chang-jiang Liu ◽  
Song Pang ◽  
Qiang Xu ◽  
Ling He ◽  
Shao-peng Yang ◽  
...  
Keyword(s):  
Boltzmann Equation ◽  
Two Phase Flow ◽  
Three Dimensional ◽  
Phase Flow ◽  
Bgk Model ◽  
Two Phase ◽  
The Boltzmann Equation

scholarly journals Boltzmann-Grad limit of a hard sphere system in a box with isotropic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Corentin Le Bihan
Keyword(s):  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Compact Domain ◽  
The Boltzmann Equation ◽  
Grad Limit ◽  
Random Direction ◽  
Time Restriction ◽  
Short Time

<p style='text-indent:20px;'>In this paper we present a rigorous derivation of the Boltzmann equation in a compact domain with {isotropic} boundary conditions. We consider a system of <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula> hard spheres of diameter <inline-formula><tex-math id="M2">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> in a box <inline-formula><tex-math id="M3">\begin{document}$ \Lambda : = [0, 1]\times(\mathbb{R}/\mathbb{Z})^2 $\end{document}</tex-math></inline-formula>. When a particle meets the boundary of the domain, it is instantaneously reinjected into the box with a random direction, {but} conserving kinetic energy. We prove that the first marginal of the process converges in the scaling <inline-formula><tex-math id="M4">\begin{document}$ N\epsilon^2 = 1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \epsilon\rightarrow 0 $\end{document}</tex-math></inline-formula> to the solution of the Boltzmann equation, with the same short time restriction of Lanford's classical theorem.</p>

Nonlinear Simulation of Interaction between Water and Free Floating Ship

2011 ◽  
Vol 90-93 ◽  
pp. 2528-2532
Author(s):  
Hong Wei Ma ◽  
Ji Wei Wang ◽  
Ji Xiang Xu
Keyword(s):  
Boundary Conditions ◽  
Stress Responses ◽  
Moving Boundary ◽  
Dynamic Responses ◽  
Water Model ◽  
Floating Body ◽  
Surface Boundary ◽  
Time Step ◽  
Two Phase ◽  
Nonlinear Simulation

Based on fluid-solid two-phase coupling numerical model, this paper utilized velocity potential function theory to investigate the nonlinear interaction of water and free floating body. Meanwhile, multi-time step integral method and Overall numerical solution method, which are suitable for finite element dynamic analysis, and free surface boundary condition, not moving boundary conditions and the water-solid coupling boundary conditions are adopted to analyze the dynamic responses of water and free floating body with different dimensions. Numerical results show that the change of floating body sizes can obviously affect the dynamic characteristics of the fluid-solid coupling system, especially in the aspects of the stress responses of the floating body and the pressure responses of the water model.

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