Equilibrium Distribution Functions in Entropic Lattice Boltzmann Method
The lattice Boltzmann method is a numerical scheme for mesoscopic description between the molecular level and the micelle level. Instabilities of lattice Boltzmann method for turbulence simulation were improved by the entropic lattice Boltzmann method. Ho
- PDF / 828,218 Bytes
- 14 Pages / 439.37 x 666.142 pts Page_size
- 90 Downloads / 225 Views
Abstract The lattice Boltzmann method is a numerical scheme for mesoscopic description between the molecular level and the micelle level. Instabilities of lattice Boltzmann method for turbulence simulation were improved by the entropic lattice Boltzmann method. However, the theoretical research of entropic lattice Boltzmann method is not yet mature, and theories of equilibrium distribution functions are divided into two schools. Aimed at high Reynolds number turbulence simulation based on the entropic lattice Boltzmann method, the entropy form, the third-order polynomial form and second-order polynomial form of equilibrium distribution functions were compared. Concerned variables contained the vertical velocity, strain rate tensor and component of equilibrium distribution functions. Conclusion: as for entropic lattice Boltzmann method for turbulence simulations, polynomial forms of equilibrium distribution function perform a significantly higher efficiency than the entropy form while the entropy form of equilibrium distribution function can achieve a higher stability.
1 Introduction As a mesoscopic method, the lattice Boltzmann method (LBM) allows people to get a particular way in mesoscopic description. It has been used in both mechanism research and applied research in many fields, including porous media [1], biological fluid [2], crystal growth [3], chemical reaction [4] and turbulence [5]. In recent years, numerical experiments have proved the potential ability of LBM dealing with many difficult problems in the field of dynamics. With characteristics of a clear background in physics and linear equations, the shortcoming of LBM is the numerical instabilities especially in high Reynolds number turbulence simulations. Thus, to improve instabilities of LBM entropic lattice Boltzmann method (ELBM) was developed. It has been an important Q. Liu (&) W. Xie Y. Wang China Ship Development and Design Center, Zhangzhidong 268, Wuhan 430064, China e-mail: [email protected] © Springer Science+Business Media Singapore 2017 X. Li et al. (eds.), Proceedings of the 7th International Conference on Discrete Element Methods, Springer Proceedings in Physics 188, DOI 10.1007/978-981-10-1926-5_60
579
580
Q. Liu et al.
research branch of LBM studies. For the theoretical research of ELBM, there are two main schools, called the Zurich school [6–9] and the Boston school [10–12]. The Zurich school deduces and uses an entropy form of equilibrium distribution function, while the Boston school deduces and uses a third-order polynomial form of equilibrium distribution function. In 2007, Keating et al. [13] carried out a comparative study of the entropy form and third-order polynomial form, but their study did not involve the second-order polynomial form of equilibrium distribution function. Taking into account of the order of LBM itself, we believe that a comparison including the second-order polynomial form is necessary. Therefore a comparative study of three different forms of equilibrium distribution functions in ELBM is presented.
Data Loading...
