A mass conserving boundary condition for the lattice Boltzmann method for tangentially moving walls

Mass and momentum transfer across solid-fluid boundaries in the lattice-Boltzmann method

“…The simulations and discussions presented in this paper are for the SRT BGK model, since all the previous studies on LMC enhancement and momentum adjustment across solid-fluid boundaries were conducted with this SRT BGK model [5,[19][20][21][22][23][24][25][26]30]. The time period of these works (1995-2011) clearly indicates that the boundary mass conservation and momentum transfer have been long-time concerns among LBM researchers, in spite of the previous analysis and clarifications [8,20,27].…”

“…To further confirm our results, a separate control-volume calculation has been performed for System B, and the drag force obtained there is 2.922 × 10 −4 , with a 0.51% relative difference. It is interesting to notice that, in previous models for boundary mass conservation [21][22][23]25,26], normal boundary movement has not been considered in those simulations, even for those models with the boundary velocity included in the formulations [22,23,25].…”

“…As we reviewed in the Introduction, typical mass conserving methods [21][22][23]25,26] apply an equal incoming-outgoing PDF-flux requirement at boundary nodes. In addition to the normal boundary movement discussed above, the unbalanced mass flux can also be introduced by the density gradient along the boundary [9,21].…”

“…In addition to the velocity accuracy at the boundary, mass transfer across a solid-fluid boundary has also been concerned [5,[19][20][21][22][23][24][25][26]. Soon after the Ladd modification of the classical BB scheme, Aidun and Lu [5] argued that the Ladd method could induce possible mass transfer across an impenetrable surface due the particular PDF correction term.…”

“…For example, Chopard and Dupuis [21] proposed to set the total PDFs outgoing from a boundary node on a flat wall to be the same as the total PDFs incoming toward the same boundary node, and this approach was later modified by Hollis et al [22] to incorporate boundary movement. On the other hand, Le Coupanec and Verschaeve [26] constructed an unknown PDF from a boundary node by calculating the nonequilibrium part from the velocity gradient and the equilibrium part from the boundary velocity and a fictitious density at the boundary node. The fictitious density was adjusted to ensure that the incoming and outgoing PDF amounts are the same at the boundary node.…”