**5. Conclusions**

In this work, two-dimensional Saint-Venant equations were implemented by using the leapfrog-style finite difference method for the purpose of studying flood behavior. Largescale heterogeneous parallel solution is implemented using MPI, OpenMP, Pthread, and OpenCL runtime libraries. The heterogeneous strategy is optimized by overlapping communication calculation, setting up work groups, etc., and performance tests from various perspectives are also carried out. Finally, a large-scale heterogeneous parallel solution for 2D SV equations with good performance is obtained. In the future, we hope that our work can become a large-scale heterogeneous parallel solution framework capable of solving SV equations -like PDE. For example, the heat conduction equation as an important PDE should also be able to use our computational framework. It describes how the temperature in a region changes with time, and like the Saint-Venant equation, it is difficult to obtain analytical solutions, and numerical methods are usually used to obtain numerical solutions. There are also some other problems that may also be able to use our computational framework, such as phase transitions, elasticity, electrical potential, etc. The purpose of our current research is to propose a massively heterogeneous parallel framework based on Saint-Venant's equations in domestic advanced computing systems. Therefore, a simple model is used to facilitate heterogeneous parallel implementation. In the future work, we will consider more complex and more types of models to simulate various actual situations (such as floods, tsunamis, dam failures, etc.).

**Author Contributions:** Conceptualization, Q.L. and N.N.; methodology, Q.L. and N.N.; software, Y.Q.; validation, L.G., W.Y. and Z.L.; formal analysis, Q.L.; investigation, Y.Q.; resources, Q.L.; data curation, Y.Q. and X.S.; writing—original draft preparation, Y.Q.; writing—review and editing, Q.L., Z.Z. and J.Z.; visualization, Y.Q. and S.T.; supervision, Q.L.; project administration, N.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key R&D Program of China (Grant No. 2020YFB1709501), GHFund A (No. 20210701) and the Shandong Province Natural Science Foundation (Grant No. ZR201910310143).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
