## 2 Description of the LBM Model and Simulation Parameters
The force density vector was set to 9810 (N/m\({}^{3}\)) along the \(x\)-axis direction, and its constant value was fixed for the whole fluid region of the hexagonal and \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter/Grid** & **Serpentine** & **Hexagonal** & **Circular** \\ \hline
**Grid parameters** & & & \\ Total number of computational nodes & 7,230,630 & 858,319 & 876,339 \\ Number of fluid (type 1) nodes & 5,866,128 & 690,651 & 705,879 \\ Number of full-way bounce-back (type 61) nodes & 32,082 & 11,094 & 9128 \\ Number of “velocity 0” (type 40) nodes & 1,326,894 & 153,478 & 158,318 \\ Number of “periodic” (type 4) nodes & 5526 & 3096 & 3014 \\ The ratio of boundary nodes to the total number & 18.87 & 19.53 & 19.45 \\ of computational nodes (\%) & & & \\ \hline
**Solution parameters** & & & \\ The free solution parameter: relaxation time, \(\tau\) & 1.0 & 1.0 & 1.0 \\ Convergence criteria: the mean scaled residue of & \(1\times 10^{-8}\) & \(1\times 10^{-8}\) & \(1\times 10^{-8}\) \\ the average velocity for subsequent iterations & & & \\ Convergence criteria: the mass flow error for & & & \\ subsequent iterations, (\%) & & & \\ \hline
**Performance data 1** & & & \\ Total number of iterations (time steps) needed to & & & \\ obtain converged solution & & & \\ Computation time (s) & 6778 & 33.3 & 33.6 \\ MLUPS (Million Lattice Updates per Second) & 39.5 & 39.5 & 39.7 \\ \hline \hline \end{tabular}  
* A personal computer equipped with Intel Core i9-9900K CPU 3.60 GHz \(\times\) 8, 32 Gb of DDR4 3000 MT/s, working under the control of Linux Min 19 Tara, was used for solving the model.  
\end{table} 
Table 1: Grid statistics, solution parameters, and performance data. Figure 8: The periodic segment of the numerical grid of the circular channel: (**a**) The whole X-Y grid topology; (**b**) The close-up view of the curved wall (square mark b); (**c**) The close-up view of the inlet region (square mark c). circular grids, while in the serpentine grid the force was set only for the red-marked region in Figure 6a along the \(x\)-axis direction. A quick glance at the performance data collected in Table 1 leads to the conclusion that a commonly used measure of code performance, MLUPS, says little about the real computation time of real-world steady-state solutions. The hexagonal and circular grids are nearly the same and give the same computation time. The serpentine grid is about 8.5 times larger than the other two. However, the computation time is 200 times longer (!) for the same solution parameters and convergence criteria as set for the hexagonal and circular grids, while the MLUPS is the same in all cases. This is because the shape of the channel is elongated, and 22.5 times more iterations are needed to propagate solution values along the grid. Long channels with low heights are standard elements of the construction of microfluidic devices. We can expect that a similar unfavorable phenomenon will accompany all of the calculations of microfluidic systems. The multigrid method or specially accelerated LBE algorithms, dedicated to steady-state solutions of flows, could solve the problem with the simulation performance drop [45].