*3.2. Rayleigh–Taylor Instability*

As a model validation, Rayleigh–Taylor Instability is investigated for two different resolutions: 256 × 1024 and 1024 × 4096. As shown in Figure 4, the computational domain consists of a heavier liquid on top impinging the bottom lighter one, with an initial single mode wave of an amplitude of 10% of the domain width. Vertical boundaries are set as periodic. The upper and lower boundaries are set as no-slip walls. Reynolds, Atwood and Bonds numbers are set as 256, 0.5 and 100, respectively. The model shows fair qualitative agreement with the work by He et al. [40] and Chiappini et al. [41]. It is worth mentioning that the surface tension was neglected in both of their works and, therefore, the Bonds numbers are not similar for all cases. Nevertheless, the Bonds number in the shown simulations is fixed for both domain resolutions. The two cases show good mesh independency except for the last time stamp, which is as issue reported and also encountered by [40,41] for both low and high Reynolds numbers, although the last time stamp of the low-resolution case is close to the one from [41], except that the bubble separation appeared slightly before our presented case.

**Figure 4.** RTI with time plotted on the same density contour levels (Re = 256, At ≈ 0.5, Bo ≈ 100). (**a**) Resolution: 256 × 1024. (**b**) Resolution: 1024 × 4096.

The selected SC interaction parameters for reaching the required density ratio and surface tension are: *G*<sup>12</sup> = *G*<sup>21</sup> = 3.15, *G*<sup>22</sup> = −3.4 and *G*<sup>22</sup> = −3.4. The kinematic viscosities of both components are kept the same (*vcomponent* <sup>1</sup> = *vcomponent* 2). The adopted wall boundary condition is based on the extrapolation scheme by Chen et al. [42], where ghost nodes are introduced behind the boundaries and unknown distribution functions are extrapolated from the inner fluid nodes. Other boundary treatments, such as the nonequilibrium extrapolation method from Guo et al. [43], showed less stability and sudden phase changes close to the walls, which is why it was avoided in the current work. Other types of boundary treatments could be material for future investigations.
