TY - JOUR
T1 - The Simplified Lattice Boltzmann Method on Non-Uniform Meshes
AU - Zhen Chen, Chang Shu & Danielle S. Tan
JO - Communications in Computational Physics
VL - 4
SP - 1131
EP - 1149
PY - 2018
DA - 2018/04
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2016-0184
UR - https://global-sci.org/intro/article_detail/cicp/11208.html
KW - Simplified lattice Boltzmann method, lattice uniformity, Lagrange interpolation, non-uniform meshes, distribution functions.
AB - <p style="text-align: justify;">In this paper, we present an improved version of the simplified lattice Boltzmann
method on non-uniform meshes. This method is based on the recently-proposed
simplified lattice Boltzmann method (SLBM) without evolution of the distribution
functions. In SLBM, the macroscopic variables, rather than the distribution functions,
are directly updated. Therefore, SLBM calls for lower cost in virtual memories and can
directly implement physical boundary conditions. However, one big issue in SLBM is
the lattice uniformity, which is inherited from the standard LBM and this makes SLBM
only applicable on uniform meshes. To further extend SLBM to non-uniform meshes,
Lagrange interpolation algorithm is introduced in this paper to determine quantities
at positions where the streaming process is initiated. The theoretical foundation of the
interpolation process is that both the equilibrium part and the non-equilibrium part of
the distribution functions are continuous in physical space. In practical implementation,
the Lagrange interpolation polynomials can be computed and stored in advance,
due to which little extra efforts are brought into the computation. Three numerical tests
are conducted with good agreements to reference data, which validates the robustness
of the present method and shows its potential for applications to non-uniform meshes
with curved boundaries.</p>