# Just-in-Time Fluid Flow Simulation on Mobile Devices Using OpenVisFlow and OpenLB
## 3 Numerical Experiments and Discussion of Results
### Conclusions  
In this paper, we present the _paint2 sim_ software for LBM simulations on mobile devices and the numerical validation of the software on an example of the Schafer test case. The simulation results are categorized into qualitative and quantitative aspects, focusing on visualization, performance, and physical accuracy. Regarding performance, we analyzed the total performance achieved by _paint2 sim_ on various mobile devices. The Samsung Galaxy A80 exhibited the lowest CPU performance among the tested devices but still provided smooth visualization with an average of 10 Mega Lattice Updates per Second (MLUPS) and no noticeable lags. On the other hand, the Samsung Galaxy S22 Ultra demonstrated impressive performance, comparable to higher-end x86 CPUs, achieving the highest MLUPS of 24 under specific conditions. However, fluctuations in performance were observed due to heat management constraints, leading to an aggressive reduction in the CPU's power output beyond short performance bursts.  
The validation of _paint2 sim_ involved qualitative and quantitative comparisons. For the qualitative validation, we replicated a well-established 2D cylinder example using a hand-drawn image and compared the results with the validated case from _OpenLB_. The flow patterns and characteristics exhibited by _paint2 sim_ were found to be in agreement with the established findings. For the quantitative validation, we compared the drag and lift coefficients of the cylinder simulation with the results from previous studies: while the drag coefficients showed minor discrepancies of around \(\sim\)10%, the lift coefficients obtained from _paint2 sim_ differed greatly. These variations can be attributed to the shape approximation of the hand-drawn cylinder and slight inaccuracies in the scanned image.  
Overall, the performance and accuracy of _paint2 sim_ on mobile devices proved to be sufficient for the intended simulation cases and to be highly competitive with full-powered x86 CPUs within a smaller power envelope. Further enhancements can be achieved through  
\begin{table}
\begin{tabular}{l c c} \hline \hline Aspect & Nvidia Shield Tablet K1 & Huawei P8 Lite \\ \hline Processor & ARM tn8 & ARM ARMv8 \\ \hline Base Frequency & **2.22** GHz & 1.71 GHz \\ \hline Single-Core Score & **207** & 166 \\ \hline MLUPS & 1.1 & **1.6** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance and spec comparison of Nvidia Shield Tablet K1 and Huawei P8 Lite. For the spec comparison and Single-Core Score Geekbench [26].  
Figure 9: Performance decline over time of _paint2 sim_. Performance is measured in Mega Lattice Updates per Second (MLUPS).  
a parallelization of the application on mobile devices, which would significantly improve performance metrics. Future work should also address the issue of performance fluctuations resulting from heat management constraints. Taking these factors into account, the digital twin and virtual laboratory features of _paint2 sim_ hold the promise of offering a valuable simulation tool for 2D computational fluid dynamics applications, allowing for on-the-go simulations.  
Conceptualization, D.T.; methodology, D.T.; software, D.T.; validation, D.T.; formal analysis, D.T.; investigation, D.T.; resources, M.J.K.; data curation, D.T.; writing--original draft preparation, D.T.; writing--review and editing, A.K., F.B., M.D. and M.J.K.; supervision, M.J.K.; project administration, M.J.K.; funding acquisition, M.J.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by The Ministry of Science, Research and the Arts of the State of Baden-Wurttemberg, grant number 34-7811.553-4/5, and by the Lattice Boltzmann Research Group  
Not applicable.  
Data Availability StatementData is contained within the article.  
The authors declare no conflicts of interest.