Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows

Multiphase curved boundary condition in lattice Boltzmann method

The boundary treatment is fundamental for modeling fluid flows especially in the lattice Boltzmann method; the curved boundary conditions effectively improve the accuracy of single-phase simulations with complex-geometry boundaries. However, the conventional curved boundary conditions usually cause dramatic mass leakage or increase when they are directly used for multiphase flow simulations. We find that the principal reason for this is the absence of a nonideal effect in the curved boundary conditions, followed by a calculation error. In this paper, incorporating the nonideal effect into the linear interpolation scheme and compensating for the interpolating error, we propose a multiphase curved boundary condition to treat the wetting boundaries with complex geometries. A series of static and dynamic multiphase simulations with large density ratio verify that the present scheme is accurate and ensures mass conservation.

Discrete effects on boundary conditions of the lattice Boltzmann method for fluid flows with curved no-slip walls

The lattice Boltzmann method (LBM) has been formulated as a powerful numerical tool to simulate incompressible fluid flows. However, it is still a critical issue for the LBM to overcome the discrete effects on boundary conditions successfully for curved no-slip walls. In this paper, we focus on the discrete effects of curved boundary conditions within the framework of the multiple-relaxation-time (MRT) model. We analyze in detail a single-node curved boundary condition [Zhao et al., Multiscale Model. Simul. 17, 854 (2019)10.1137/18M1201986] for predicting the Poiseuille flow and derive the numerical slip at the boundary dependent on a free parameter as well as the distance ratio and the relaxation times. An approach by virtue of the free parameter is then proposed to eliminate the slip velocity while with uniform relaxation parameters. The theoretical analysis also indicates that for previous curved boundary schemes only with the distance ratio and the halfway bounce-back (HBB) boundary scheme, the numerical slip cannot be removed with uniform relaxation times virtually. We further carried out some simulations to validate our theoretical derivations, and the numerical results for the case of straight and curved boundaries confirm our theoretical analysis. Finally, for fluid flows with curved boundary geometries, resorting to more degrees of freedom from the boundary scheme may have more potential to eliminate the discrete effect at the boundary with uniform relaxation times.

Hydrodynamic forces on monodisperse assemblies of axisymmetric elongated particles: Orientation and voidage effects

We investigate the average drag, lift, and torque on static assemblies of capsule‐like particles of aspect ratio 4. The performed simulations are from Stokes flow to high Reynolds numbers (0.1 ≤ Re ≤ 1,000) at different solids volume fraction (0.1 ≤ ɛ_s ≤ 0.5). Individual particle forces as a function of the incident angle ϕ with respect to the average flow are scattered. However, the average particle force as a function of ϕ is found to be independent of mutual particle orientations for all but the highest volume fractions. On average, a sine‐squared scaling of drag and sine‐cosine scaling of lift holds for static multiparticle systems of elongated particles. For a packed bed, our findings can be utilized to compute the pressure drop with knowledge of the particle‐orientation distribution, and the average particle drag at ϕ = 0° and 90°. We propose closures for average forces to be used in Euler–Lagrange simulations of particles of aspect ratio 4.