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

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Figure 1

One-dimensional representation of a regular lattice and a curved-wall boundary.

Figure 2

Simulation setup for flow around a square obstacle, driven by gravity.

Figure 3

Change in system mass ($m^{\prime }$) for different obstacle positions ($C_x$), for (a) $\text{Re}=150$ (steady flow) and (b) $\text{Re}=330$ (unsteady flow). It should be noted that the scales are different for different $\text{Re}$. The data for Q-Bouzidi and Yin-Zhang schemes are available only for $C_x=50$ and 51.

Figure 4

Normalized flow rate ($Q^{\prime }$) for different obstacle positions ($C_x$), for (a) $\text{Re}=150$ (steady flow) and (b) $\text{Re}=330$ (unsteady flow).

Figure 5

Normalized drag ($F_D^{\prime }$) for different obstacle positions ($C_x$), for (a) $\text{Re}=150$ (steady flow) and (b) $\text{Re}=330$ (unsteady flow).

Figure 6

Change in system mass ($m^{\prime }$) for different obstacle positions ($C_x$), for (a) $\text{Re}=150$ (steady flow) and (b) $\text{Re}=330$ (unsteady flow).

Figure 7

Normalized flow rate ($Q^{\prime }$) for different obstacle positions ($C_x$), for (a) $\text{Re}=150$ (steady flow) and (b) $\text{Re}=330$ (unsteady flow).

Figure 8

Normalized drag ($F_D^{\prime }$) for different obstacle positions ($C_x$), for (a) $\text{Re}=150$ (steady flow) and (b) $\text{Re}=330$ (unsteady flow).

Figure 9

Distribution of horizontal velocity component $U_x$ for different schemes.

Figure 10

The normalized system mass ($m^{\prime }$) of different schemes for the inclined channel flow over time.

Figure 11

The normalized tangential velocity ($U^{*}$) of the flow inside a straight channel with an inclination of $3/5$. (b) Zoom-in of the full velocity profile shown in (a).

Figure 12

The staggered cylinder configuration: The domain is periodic and the flow is driven by gravity.

Figure 13

The accurate velocity field for $\text{Re}=40$ obtained using the mid-grid bounce-back scheme with very high grid resolution.

Figure 14

The normalized system mass ($m^{\prime }$) of different schemes for the periodic flow around staggered cylinders.

Figure 15

The normalized drag ($F_D^{\prime }$) of different schemes for the periodic flow around staggered cylinders. It should be noted that $F_D^{\prime }$ of L-Bouzidi scheme, though it appears closest to 1, is time dependent. This implies a longer simulation would result in $F_D^{\prime }$ further away from 1. Only the results of cases 1–5 and MGBB are time independent.