The problem of fluid compressibility in the ordinary approach to lattice Boltzmann (LB) according to the BGK method is analyzed. A new velocity is introduced besides the usual one, linked to this later by a dimensionless mass density. The LBGK method based on this second velocity, with a suitable second order equilibrium distribution (different from the ordinary one), leads to the real Navier–Stokes equation of incompressible fluids under the steady mass density condition. This approach is compared with two well known methods one can found in literature. Finally, the role of the approach introduced here and of the ordinary one with respect to Poiseuille flow simulation is presented.
Cattaneo, G., Dennunzio, A., Farina, F. (2004). Lattice Boltzmann Approach to Incompressible Fluidynamics Dimensional Investigation and Poiseuille Test. In Cellular Automata 6th International Conference on Cellular Automata for Research and Industry, ACRI 2004 (pp.871-880). Springer Verlag [10.1007/978-3-540-30479-1_90].
Lattice Boltzmann Approach to Incompressible Fluidynamics Dimensional Investigation and Poiseuille Test
CATTANEO, GIANPIERO;DENNUNZIO, ALBERTO;FARINA, FABIO MARIO
2004
Abstract
The problem of fluid compressibility in the ordinary approach to lattice Boltzmann (LB) according to the BGK method is analyzed. A new velocity is introduced besides the usual one, linked to this later by a dimensionless mass density. The LBGK method based on this second velocity, with a suitable second order equilibrium distribution (different from the ordinary one), leads to the real Navier–Stokes equation of incompressible fluids under the steady mass density condition. This approach is compared with two well known methods one can found in literature. Finally, the role of the approach introduced here and of the ordinary one with respect to Poiseuille flow simulation is presented.
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