@Article{AAMM-9-1,
author = {Z., Chen and Shu, C. and Y., Wang and Yang, M., L. and Tan, D.},
title = {A Simplified Lattice Boltzmann Method Without Evolution of Distribution Function},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {1},
pages = {1--22},
abstract = {<p style="text-align: justify;">In this paper, a simplified lattice Boltzmann method (SLBM) without evolution
of the distribution function is developed for simulating incompressible viscous
flows. This method is developed from the application of fractional step technique
to the macroscopic Navier-Stokes (N-S) equations recovered from lattice Boltzmann
equation by using Chapman-Enskog expansion analysis. In SLBM, the equilibrium
distribution function is calculated from the macroscopic variables, while the
non-equilibrium distribution function is simply evaluated from the difference of two
equilibrium distribution functions. Therefore, SLBM tracks the evolution of the macroscopic
variables rather than the distribution function. As a result, lower virtual memories
are required and physical boundary conditions could be directly implemented.
Through numerical test at high Reynolds number, the method shows very nice performance
in numerical stability. An accuracy test for the 2D Taylor-Green flow shows
that SLBM has the second-order accuracy in space. More benchmark tests, including
the Couette flow, the Poiseuille flow as well as the 2D lid-driven cavity flow, are conducted
to further validate the present method; and the simulation results are in good
agreement with available data in literatures.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2016-0029},
url = {https://global-sci.com/article/73236/a-simplified-lattice-boltzmann-method-without-evolution-of-distribution-function}
}