Computational fluid dynamics (CFD) is a discipline that solves and analyzes fluid dynamics problems through computer and numerical simulation methods. In the process of CFD numerical simulations, the complexity of the problem is gradually increasing, the accuracy of the numerical simulation is becoming more and more demanding, and the network size is continuously expanding. Load-balancing algorithms for CFD parallel computing are being gradually and extensively researched in the world.

Computational fluid dynamics (CFD) ^{[1]} is a discipline that solves and analyzes fluid dynamics problems through computer and numerical simulation methods. In the process of CFD numerical simulations, the complexity of the problem is gradually increasing, the accuracy of the numerical simulation is becoming more and more demanding, and the network size is continuously expanding. In the process of numerical simulations, the computational area is discretized into multiple grid blocks of different sizes, and these blocks are assigned to different processors for parallel computation. Therefore, how to make the load task of each processor reasonably balanced is the main problem to be solved, and it is also an important technology to improve the processing efficiency. As the scale of computation increases, the impact of the communication overhead of the processors is also gradually increasing on the parallel processing efficiency. The mismatch between the number of grid blocks and the number of processes, as well as the mismatch between the computational capacity of grid blocks and the computational capacity of processes, makes the traditional partitioning or combination strategies unable to meet the demand of load balancing well ^{[2]}. Therefore, the research on algorithms for large-scale load balancing is crucial.

At present, load-balancing algorithms for CFD parallel computing are being gradually and extensively researched in the world. For example, the load-balancing algorithm of greedy method and the recursive pairwise edge splitting load-balancing algorithm proposed by Streng ^{[3]} and Ytterström ^{[4]} are classical load-balancing algorithms based on a geometric level. In addition, Hendrickson et al. ^{[5]} proposed a multi-level algorithm for partitioning graphs, which is a method of mapping to a refined graph by coarsening the graph dissection. In recent years, heuristic algorithms have also been increasingly used in the research of load-balancing algorithms. Most of them are swarm intelligence algorithms that imitate natural bodies, such as firefly algorithm, ant colony algorithm, and bee colony algorithm. They are applied to solve various optimization scheduling problems and are widely used in industry ^{[6]}, network transmission ^{[7]}, biology ^{[8]} and cloud computing ^{[9]}. Among them, the combination of neural networks and other algorithms has achieved considerable research success in image capture and retrieval [10,11,12,13]^{[10][11][12][13]}. With the development of parallel computing, the improvement and optimization of heuristic algorithms to solve the load-balancing problem of parallel computing have also achieved considerable results. For example, Kernighan et al. ^{[14]} proposed a heuristic algorithm for graph segmentation. The hybrid load-balancing algorithm proposed by Yang Chengfu et al. ^{[15]} and the ant colony optimization based MrLBA algorithm proposed by Arfa Muteeh ^{[16]} are typical methods of heuristic algorithms applied to load balancing. However, swarm intelligence algorithms generally easily fall into local optimum, and the optimization effect is uneven. This preseaperrch uses the multi-level graph segmentation algorithm of a structural grid to obtain a network coarsening graph and proposes a FaCO algorithm based on the firefly and ant colony algorithm to subdivide the coarsening graph. Based on the fusion of the two in the optimization rule, a new optimization rule is established to adjust the position update, which avoids falling into the local optimal situation to a certain extent.

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