# A Heterogeneous Parallel Algorithm for Euler-Lagrange Simulations of Liquid in Supersonic Flow
## 4 Conclusions  
In the present work, a two-phase CPU/GPU heterogeneous parallel computation mode based on the Euler-Lagrange approach is established to simulate gas-liquid supersonic flows. The main conclusions are as follows. 1. Taking full advantage of CPU and GPU, an efficient parallel model for simulation of a liquid jet in supersonic flow is developed, in which the data-intensive and highly parallel tasks such as the kernel computation of gas phase and liquid phase are implemented on GPU, whereas the logical and data dependent tasks like the data transfer and general control are executed on CPU. 2. An effective method for droplet dynamic management and efficient calculation on the CPU/GPU model is proposed, in which a redundantly allocated array on the GPU  
Figure 13: The partition of time cost for the main calculation steps of the droplet phase calculation. and the CPU is used to manage and calculate the simulated droplets, and a method based on the two-pointer method is applied to subtract the disappeared droplets. 3. A droplet-locating algorithm is developed, in which a determination criterion based on scalar product and a search approach by traveling through the neighboring cell is applied to address the cell. 4. Simulation of a liquid jet in supersonic crossflow is implemented to verify the reliability of the CPU/GPU mode. The result agrees well with the experiment. 5. A simulation of a jet spray in supersonic flow is executed using CPU mode and CPU/GPU mode, respectively, to analyze the method's efficiency and limitations. Although the speedup diminishes with increasing droplet number, the benefit is still very substantial even for the worst-case scenario studied, i.e., when the ratio of droplets to grids is 1.5, the overall speedup is 20.2. Although the two-phase CPU/GPU heterogeneous parallel computation mode based on the Euler-Lagrange approach proposed in this paper is used for liquid in supersonic flow, it is also applicable to other Euler-Lagrange simulations. Conceptualization, X.L., M.S. and H.W. ; methodology, X.L. and P.L. ; software, X.L., M.S., H.W., C.W., D.X. and P.L. ; validation, X.L., C.W., G.Z. and Y.Y. ; formal analysis, X.L., H.W. and P.L. ; investigation, X.L., H.W. and P.L. ; resources, H.W., P.L., M.S. and Y.Y. ; data curation, X.L. and H.W. ; writing--original draft preparation, X.L. ; writing--review and editing, H.W., P.L., D.X. and G.Z. ; visualization  
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