共查询到20条相似文献,搜索用时 15 毫秒
1.
Shiyi Chen Zheng Wang Xiaowen Shan Gary D. Doolen 《Journal of statistical physics》1992,68(3-4):379-400
The recent development of the lattice gas method and its extension to the lattice Boltzmann method have provided new computational schemes for fluid dynamics. Both methods are fully paralleled and can easily model many different physical problems, including flows with complicated boundary conditions. In this paper, basic principles of a lattice Boltzmann computational method are described and applied to several three-dimensional benchmark problems. In most previous lattice gas and lattice Boltzmann methods, a face-centered-hyper-cubic lattice in four-dimensional space was used to obtain an isotropic stress tensor. To conserve computer memory, we develop a model which requires 14 moving directions instead of the usual 24 directions. Lattice Boltzmann models, describing two-phase fluid flows and magnetohydrodynamics, can be developed based on this simpler 14-directional lattice. Comparisons between three-dimensional spectral code results and results using our method are given for simple periodic geometries. An important property of the lattice Boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency, while all other methods, including the spectral method, are unable to model complicated geometries efficiently. 相似文献
2.
In this paper we address the problem of the time evolution of a perturbation around a steady base flow with the use of the lattice Boltzmann method (LBM). This approach, named base flow lattice Boltzmann method, is of great interest in particular for aeroacoustic fields where the acoustic perturbation, on the one hand, is almost exclusively influenced by the large scale average structures of the underlying flow, and on the other hand, has a low effect on the large structures. The method is implemented for weakly compressible flows and the results of the base flow lattice Boltzmann are compared with the standard single relaxation time LBM. The boundary conditions for the base flow lattice Boltzmann method are discussed, as well as the implementation of outflow conditions for acoustic waves. 相似文献
3.
The resistance between any two lattice points in an infinite,centered-triangular lattice of equal resistors is determined using the lattice Green function method.It is shown that the two-point resistance on the centeredtriangular lattice is expressed in terms of the resistance of a triangular lattice.Some exact values for the resistance near the origin of the lattice are presented.For large separation between lattice points the asymptotic forms of the resistance are calculated. 相似文献
4.
The accurate and efficient computation of lattice sums for the three-dimensional Helmholtz equation is considered for the cases where the underlying lattice is one- or two-dimensional. We demonstrate, using careful numerical computations, that the reduction method, in which the sums for a two-dimensional lattice are expressed as a sum of one-dimensional lattice sums leads to an order-of-magnitude improvement in performance over the well-known Ewald method. In the process we clarify and improve on a number of results originally formulated by Twersky in the 1970s. 相似文献
5.
6.
B. W. Southern 《Zeitschrift für Physik B Condensed Matter》1978,30(1):61-64
The interface free energy of an Ising model with nearest neighbour interactions on a generalized square lattice is calculated using a simple method suggested by Müller-Hartmann and Zittartz. For certain values of the coupling constants this lattice can be made to be topologically equivalent to either a hexagonal or triangular lattice. The method of calculation bypasses the full bulk problem by considering only special interface configurations of the spins. It is shown that a large number of exactly known results for these different types of lattice can be obtained using this simple method. 相似文献
7.
A method for generating vector-value integrable analogies of integrable lattice systems or integrable differential-difference equations is presented. The basic ingredient of the method is to insert permutation matrices. We formulate the zero-curvature representations and Hamiltonian structures of the resulting vector lattice systems. The effectiveness of the method is illustrated using some examples such as the Volterra lattice, the Belov–Chaltikian lattice, the Ablowitz–Ladik lattice and the Heisenberg ferromagnet lattice. 相似文献
8.
《Physica A》1987,144(1):118-127
The dimer problem on a two-dimensional lattice is reduced to a problem of random walks on the lattice, and then the latter problem is solved by the method which Vdovichenko developed in order to derive an exact expression for the partition function of the Ising model on a two-dimensional lattice. The result for the generating function is identical to the usual result for the general lattice. For loose-packed lattices such as the square and the honeycomb lattice on a torus, it takes the form of a linear combination of four determinants, where no problem of determining signs occurs. 相似文献
9.
V. A. Nepochatenko 《Bulletin of the Russian Academy of Sciences: Physics》2007,71(10):1358-1361
A new method for determining the lattice parameters near the first-order phase transition is proposed. The method is based on the model of a thin phase boundary and a linear dependence between the lattice parameters within a phase. 相似文献
10.
The affection on the nature of percolation by concentration of pentagon–heptagon defects in graphene lattice 下载免费PDF全文
In this paper the percolation behavior with a specific concentration of the defects was discussed on the twodimensional graphene lattice. The percolation threshold is determined by a numerical method with a high degree of accuracy. This method is also suitable for locating the percolation critical point on other crystalline structures. Through investigating the evolution of the largest cluster size and the cluster sizes distribution, we find that under various lattice sizes and concentrations of pentagon-heptagon defects there is no apparent change for the percolation properties in graphene lattice. 相似文献
11.
A method is suggested for derivation of the Bethe ansatz equations for the six-vertex model on a square lattice rotated at an arbitrary angle with respect to the coordinate axes. The method is based on the random walk representation for configurations of the model. The equations for the ice model on the rotated lattice are derived and some numerical results are obtained. 相似文献
12.
《Physica A》2006,362(1):6-10
A direct numerical simulation of a turbulent flow field with a lattice BGK method is presented. A spatial coarse graining of the numerical results is compared with the expected LBGK dynamics for a flow field on a reduced lattice size. This comparison permits to exhibit subgrid properties of the fluid which are not resolved on the coarse lattice. As expected from existing subgrid models, an effective viscosity can be measured that increases when the lattice is coarse grained. Turbulence models based on an effective viscosity are particularly interesting in a lattice Boltzmann simulation, due to the linearity of the propagation operator. 相似文献
13.
Arzhang AngoshtariArash Yavari 《Physics letters. A》2011,375(10):1281-1285
A rigorous proof for convergence of the Wolf method (Wolf et al., 1999 [9]) for calculating electrostatic energy of a periodic lattice is presented. In particular, we show that for an arbitrary lattice of unit cells, the lattice sum obtained via Wolf method converges to the one obtained via Ewald method. 相似文献
14.
REN Hongwu FANG Zhujie 《Chinese Journal of Lasers》1999,8(6):525-530
1 Introduction Opticaltomographyprovidesanalternativetechnologytoprobebreastcancerandmonitorhumantissue’sfunctionalparameternoninvasively[1,2].Photonmigrationintissueplaysakeyroleinopticaltomography.Recently,alatticerandomwalkmodel[3,4]isemployedtod… 相似文献
15.
A lattice random walk model based on particles scattering on discrete lattice of homogenous space is introduced. The discrete Green's function (DFG) for two-dimensional and three-dimensional lattice random walk of photon is found and proved by mathematical induction. The convolution theorem of photon lattice random walk is presented. They can be used with the method of images to calculate the photon density distribution in semi-infinite and finite slab homogenous turbid media such as tissue. 相似文献
16.
A. Ŝurda 《Zeitschrift für Physik B Condensed Matter》1982,46(4):371-374
A noncombinatorial variation method for calculation of thermodynamic and correlation functions in a wide class of lattice models is developed. The method is illustrated on the model of a two-dimensional lattice gas consisting ofM kinds of molecules with pairwise interaction. 相似文献
17.
Diffusion on random systems above and at their percolation threshold in three dimensions is carried out by a molecular trajectory method and a simple lattice random walk method, respectively. The classical regimes of diffusion on percolation near the threshold are observed in our simulations by both methods. Our Monte Carlo simulations by the simple lattice random walk method give the conductivity exponent μ/ν=2.32±0.02 for diffusion on the incipient infinite clusters and μ/ν=2.21±0.03 for diffusion on a percolating lattice above the threshold. However, while diffusion is performed by the molecular trajectory algorithm either on the incipient infinite clusters or on a percolating lattice above the threshold, the result is found to be μ/ν=2.26±0.02. In addition, it takes less time step for diffusion based on the molecular trajectory algorithm to reach the asymptotic limit comparing with the simple lattice random walk. 相似文献
18.
In the Monte Carlo simulation of QCD, the euclidean form of the partition function is evaluated on a finite lattice. We use this method to calculate the partition function for non-interacting Bose and Fermi fields. Here the expressions on the lattice can be evaluated in closed form and the continuum limit is well-known; this provides us with a measure for finite lattice size effects in such approaches. 相似文献
19.
《Physics letters. [Part B]》1999,463(1):63-68
The axial anomaly of lattice abelian gauge theory on a hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory. 相似文献