Test of the Possible Application of the Half—Way Bounce—Back Boundary Condition for Lattice Boltzmann Methods in Complex Geometry

The way of handling boundary conditions with simple bounce-back rule in the lattice gas and lattice Boltzmann method had been considered as one of the advantage compared with other numerical schemes,The half-way bounce-back rule inherits the advantage of the bounce-back rule and improves the accuracy to the second-order on flat boundaries,In this paper,we test the possible application of the half-way bounce-back rule to the system with complex geometry,Our simulation results show that the half-way bounce-back rule is a good boundary condition in the problems without emphasis on accuracy.     

Lattice Boltzmann method with the cell-population equilibrium

The central problem of the lattice Boltzmann method （LBM） is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non- negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman-Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.     

A Multigrid-Solver for the Discrete Boltzmann Equation

This paper introduces a nonlinear multigrid solution approach for the discrete Boltzmann equation discretized by an implicit second-order Finite Difference scheme. For simplicity we restrict the discussion to the stationary case. A numerical example shows the drastically improved efficiency in comparison to the widely used Lattice–Bathnagar–Gross–Krook (LBGK) approach.     

Path-integral quantization of Galilean Fermi fields

The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. First, we review the five-dimensional approach to the Galilean Dirac equation, which leads to the Lévy-Leblond equations, and define the Galilean generating functional and Green’s functions for positive- and negative-energy/mass solutions. Then, as an example of interactions, we consider the quartic self-interacting potential , and we derive expressions for the 2- and 4-point Green’s functions. Our results are compatible with those found in the literature on non-relativistic many-body systems. The extended manifold allows for compact expressions of the contributions in (3 + 1) space-time. This is particularly apparent when we represent the results with diagrams in the extended (4 + 1) manifold, since they usually encompass more diagrams in Galilean (3 + 1) space-time.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.     

Axiomatic Foundations of Galilean Quantum Field Theories

A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use of certain mathematical theories, such as group theory and the theory of rigged Hilbert spaces. Our approach regards the fields as real things with symmetry properties. The general structure is analyzed and contrasted with relativistic theories.On leave of absence from     

Weak-field approximation of effective gravitational theory with local Galilean invariance

We examine the weak-field approximation of locally Galilean invariant gravitational theories with general covariance in a (4+1)-dimensional Galilean framework. The additional degrees of freedom allow us to obtain Poisson, diffusion, and Schrödinger equations for the fluctuation field. An advantage of this approach over the usual (3+1)-dimensional General Relativity is that it allows us to choose an ansatz for the fluctuation field that can accommodate the field equations of the Lagrangian approach to MOdified Newtonian Dynamics (MOND) known as AQUAdratic Lagrangian (AQUAL). We investigate a wave solution for the Schrödinger equations.     

一个新的用于不可压磁流体动力学的格子波尔兹曼模型

绝大多数现有的格子波尔兹曼磁流体动力学模型其实是用可压缩方法来模拟不可压磁流体。而这些可压缩效应在数值模拟中往往会带来意想不到的误差。在这篇文章中,我们提出了一个全新的可用于的不可压格子波尔兹曼磁流体动力学模型,并且进行了哈特曼流的数值模拟。模拟结果与哈特曼流的解析解非常吻合。这个方法需要一个假设条件来消除误差。我们做了大量的数值试验,并且与Dellar教授的模型进行了详细的分析与比较。     

用晶格玻尔兹曼方法研究颗粒在涡流中的运动

用晶格玻尔兹曼方法研究小颗粒在涡流中的运动.涡流由流经空腔的流体产生.用动量交换法和压力张量积分法计算颗粒在涡流中的运动轨迹、速度和角速度.最后用张量积分法计算两个不同半径的颗粒在涡流中的运动.关键词：晶格玻尔兹曼方法涡流颗粒     

格子Boltzmann方法对Rayleigh-Benard流的模拟与非线性分析

本文利用格子Boltzmann方法对不同Ra下的Rayleigh-Benard自然对流进行了数值模拟,得到的Nu与前人的结果一致。数值结果表明,Ra=2000时,格子Boltzmann方法得到了三个静态分岔解,其中一个为非稳定解;在Ra=5×10~5时格子Boltzmann方法得到了类似于周期的振荡解。本文采用插值格子Boltzmann方法,在Ra=2000,取不同插值节点进行计算时,得到了一种非稳态解。     

液滴撞击液膜过程的格子Boltzmann方法模拟

本文采用格子Boltzmann方法对液滴撞击液膜过程进行了研究, 主要考察了雷诺数(Re)、韦伯数(We)、相对液膜厚度 (h) 以及表面张力 (σ) 等物理参数对界面运动过程的影响. 首先, 随着Re数和We数的增加, 可以明显观察到液滴撞击液膜过程中形成的皇冠状水花以及卷吸现象; 当Re数较大时, 液体会发生飞溅, 由液体飞溅形成的小液滴则会继续下落, 并与液膜再次发生碰撞. 其次, 当相对液膜厚度较小时, 液滴撞击液膜并最终导致液膜断裂; 然而随着相对液膜厚度的增大, 尽管撞击过程溅起的液体会越来越多, 但是液膜并不会发生断裂. 再次, 随着表面张力的增大, 界面变形阻力增大, 撞击过程中产生的界面形变也逐渐减弱. 最后还发现皇冠(由液滴溅起形成)半径r 随时间满足r/(2R) ≈ α√Ut/(2R), 这一结果与已有结论是一致的.