## 1 Introduction
To achieve larger-scale computations, algorithms in multi-GPU heterogeneous environments have received more attention. [PERSON] et al. [20] utilized the characteristics of multi-stream processors to achieve large-scale parallel computing in multi-GPU environments by hiding the communication time between the CPU and GPU. Subsequently, [PERSON] et al. [21] further partitioned the computational grid using MPI parallelism to solve larger-scale grids with multiple GPUs. [PERSON] et al. [22] implemented heterogeneous parallel acceleration of LBM on the Tsubame 2.0 supercomputer using GPUs and tested strong and weak scalability with more than 1000 GPUs. [PERSON] et al. [23] implemented and optimized the LBM open-source code openLBMflow on the Tianhe-2 supercomputer using the Intel Xeon Phi coprocessor (MIC) for acceleration. Scalability tests were conducted using 2048 nodes. [PERSON] et al. [24] developed a complete LBM software, SunwayLB, on the Sunway TaihuLight supercomputer cluster, covering the entire process from preprocessing to computation. Its acceleration performance is up to 137 times faster, making large-scale industrial applications and real-time simulations of LBM possible. [PERSON] et al. [25] implemented a fully scalable LBM method for CPU/GPU heterogeneous clusters. They used the Piz Daint CPU/GPU heterogeneous cluster with 24,576 CPU cores and 2048 GPU cards, achieving a grid size of up to 680 million. [PERSON] et al. [26] simulations have demonstrated good weak scaling up to 16,384 nodes and achieved a high performance of 10.9 PFLOPS in single precision. [PERSON] et al. [27] proposed a parallel DEM-IMB-LBM framework based on the Message Passing Interface (MPI). This framework employs a static domain decomposition scheme, partitioning the entire computational domain into multiple subdomains according to predefined processors. The framework was then applied to simulation scenarios of multi-particle deposition and submarine landslides. In addition, many scholars have conducted parallel studies on various applications of the LBM [28; 29; 30; 31; 32; 33]. This paper implements a multi-node, multi-DCU heterogeneous parallel framework on the \"Dongfang\" supercomputing system. This framework's design differs from those of other researchers and demonstrates good parallel efficiency, which can provide a valuable reference for other researchers. Although the manuscript primarily reports 2D simulation results, we believe that the use of the hardware and its performance optimization still hold innovation and reference value. In this study, the correctness and effectiveness of the LBM heterogeneous parallel algorithm were validated through lid-driven cavity flow using the D2Q9 model of the single relaxation time LBM. Subsequently, optimization and performance testing were conducted, resulting in a parallel efficiency of over 90%. The following aspects were primarily focused on:  
Firstly, a heterogeneous parallel algorithm for LBM was implemented using the cross-platform parallel programming model OpenCL. This implementation enables LBM simulations to be executed in parallel on various computing hardware, effectively utilizing the computational resources of different architectures. Secondly, to reduce the communication overhead on the CPU side and the memory access overhead on the DCU side, some optimization strategies, such as non-blocking communication, utilization of high-speed shared memory, and coalesced access, were adopted. These strategies effectively manage data transmission and memory access. Finally, the performance testing demonstrates that by adjusting the computational grid size on the CPU to be 1/10 of that on a single DCU, a computational balance between the CPU and DCU can be achieved. This adjustment allows the computation time on the CPU and DCU to overlap, fully utilizing the available computational resources.