Simulation of gas dynamics with the lattice Boltzmann method
Authors
N.E. Grachev
A.V. Dmitriev
D.S. Senin
Keywords:
gas dynamics
computer simulation
lattice Boltzmann method
Abstract
A computer implementation of a method to simulate the motion of a single-phase one-component viscous gas in three dimensions is considered. The method is based on the application of the lattice Boltzmann equations. The method has a number of advantages compared with the approach of describing the gas dynamics on the basis of the Navier-Stokes equations. A verification of this computer implementation is performed. The numerical results are compared with the corresponding analytical dependencies.
Sun C. Lattice-Boltzmann models for high speed flows // Phys. Rev. E. 1998. 58, N 6. 7283-7287.
Chen F., Xu A., Zhang G., Li Y. Three-dimensional lattice Boltzmann model for high-speed compressible flows // Commun. Theor. Phys. 2010. 54, N 6. 1121-1128.
He X., Luo L.-S. Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation // Phys. Rev. E. 1997. 56, N 6. 6811-6817.
Begum R., Basit M.A. Lattice Boltzmann method and its applications to fluid flow problems // European J. of Scientific Research. 2008. 22, N 2. 216-231.
Bhatnagar P., Gross E.P., Krook M.K. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems // Phys. Rev. 1954. 94, N 3. 511-525.
Qian Y.H., d’Humiéres D., Lallemand P. Lattice BGK models for Navier-Stokes equation // Europhysics Letters. 1992. 17, N 6. 479-484.
Mei R., Yu D., Shyy W., Luo L.-S. Force evaluation in the lattice Boltzmann method involving curved geometry // Phys. Rev. E. 2002. 65, N 4. 041203/1-14.
Estallo S.I. Computational gas dynamics with the lattice Boltzmann method: preconditioning and boundary conditions. University of Zaragoza. Zaragoza, 2008.
Mattila K. Implementation techniques for the lattice Boltzmann method. University of Jyväskylä. Jyväskylä, 2010.
Wolf-Gladrow D.A. Lattice-gas cellular automata and lattice Boltzmann models. An introduction. Berlin: Springer, 2005.
Succi S. The lattice Boltzmann equation for fluid dynamics and beyond. Oxford: Clarendon Press, 2001.