# A Deep Learning-Based Mapping Model for Three-Dimensional Propeller RANS and LES Flow Fields
## 4 Experiments
### Discussion
Finally, relying on data-driven mapping methods, the model is able to fill in the missing turbulence information of RANS so that the predicted LES flow field contains abundant fine vortices and turbulent structures and achieves an approximation of LES details. Fourthly, it should be ensured that the simulation data had sufficient density and resolution to accurately represent the physical phenomenon. This is inherent to LES. However, in order to apply the RANS technique, we can convert RANS data into three-dimensional image data by voxelization to meet the input requirements of the neural network. Specifically, in the data preprocessing stage, the RANS data is cropped and voxelized, and the velocity information in each spatial region is densely sampled and rearranged to generate a fine-grained three-dimensional voxel grid. This method improves the density and accuracy of the data. In this way, even if the RANS data has a low resolution, by comparing it with high-resolution LES data during training, the model can learn the mapping relationship between RANS and LES and then generate a flow field close to the LES resolution. Through this data density processing, the authors partially compensated for the limitations of RANS in detail expression, making it closer to the effect of LES in resolution. Fifthly, this work mainly considers the mapping problem from the perspective of deep learning and has not conducted in-depth research on the actual solution of the N-S equation. The main purpose of the work is to maintain the computational efficiency of RANS while generating prediction results close to the LES level so as to achieve efficient numerical simulation under complex flow fields. Sixthly, this paper uses the weighted average of 27 neighboring points to calculate the velocity, which has some defects. Weighted averaging may lead to the loss of local details, especially in turbulent areas or high gradient areas, where the velocity changes greatly, and simple weighted averaging can blur the small-scale fluid features. In addition, boundary effects may also affect the accuracy of weighted averaging. For example, near blades or walls, sparse data may lead to inaccurate calculations at the boundaries. To solve these problems, some improvement methods can be considered. To address the problem of local detail loss, adaptive weight allocation can be used to adjust the weights according to the gradient or the complexity of the local flow field and reduce the weights in high-gradient areas to retain small-scale details. In terms of boundary effects, mirror interpolation or boundary extension methods can be used to generate symmetric data or virtual points at the boundary to reduce boundary errors. Finally, as for the model application in a specific industry, since this model is based on deep neural networks with integration of regression algorithms, it maintains the high-accuracy predictions of LES while leveraging the lower computational cost of RANS and also has good generalization ability. When it is used for engineering applications involving high Reynolds numbers and complex geometries, such as ship propellers, the model's generalization capability can be improved by expanding the training samples from the specific flow fields and also incorporating additional physical constraints.