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Numerical modeling of turbulent flows requires finding the balance between accuracy and computational efficiency. For example, DNS and LES models allow to obtain more accurate results, comparing to RANS models, but are more computationally expensive. Because of this, modern applied simulations are mostly performed with RANS models. But even RANS models can be computationally expensive for complex geometries or series simulations due to the necessity of resolving the boundary layer. Some methods, such as wall functions and near-wall domain decomposition, allow to significantly improve the speed of RANS simulations. However, they inevitably lose precision due to using a simplified model in the near-wall domain. To obtain a model that is both accurate and computationally efficient, it is possible to construct a surrogate model based on previously made simulations using the precise model.

In this paper, an operator is constructed that allows reconstruction of the flow field obtained by an accurate model based on the flow field obtained by the simplified model. Spalart–Allmaras model with approximate nearwall domain decomposition and Spalart–Allmaras model resolving the near-wall region are taken as the simplified and the base models respectively. The operator is constructed using a local approach, i. e. to reconstruct a point in the flow field, only features (flow variables and their derivatives) at this point in the field are used. The operator is constructed using the Random Forest algorithm. The efficiency and accuracy of the obtained surrogate model are demonstrated on the supersonic flow over a compression corner with different values for angle $\alpha$ and Reynolds number. The investigation has been conducted into interpolation and extrapolation both by $Re$ and $\alpha$.

When modeling turbulent flows in practical applications, it is often necessary to carry out a series of calculations of bodies of similar topology. For example, bodies that differ in the shape of the fairing. The use of convolutional neural networks allows to reduce the number of calculations in a series, restoring some of them based on calculations already performed. The paper proposes a method that allows to apply a convolutional neural network regardless of the method of constructing a computational mesh. To do this, the flow field is reinterpolated to a uniform mesh along with the body itself. The geometry of the body is set using the signed distance function and masking. The restoration of the flow field based on part of the calculations for similar geometries is carried out using a neural network of the UNet type with a spatial attention mechanism. The resolution of the nearwall region, which is a critical condition for turbulent modeling, is based on the equations obtained in the nearwall domain decomposition method.

A demonstration of the method is given for the case of a flow around a rounded plate by a turbulent air flow with different rounding at fixed parameters of the incoming flow with the Reynolds number $Re = 10^5$ and the Mach number $M = 0.15$. Since flows with such parameters of the incoming flow can be considered incompressible, only the velocity components are studied directly. The flow fields, velocity and friction profiles obtained by the surrogate model and numerically are compared. The analysis is carried out both on the plate and on the rounding. The simulation results confirm the prospects of the proposed approach. In particular, it was shown that even if the model is used at the maximum permissible limits of its applicability, friction can be obtained with an accuracy of up to 90%. The work also analyzes the constructed architecture of the neural network. The obtained surrogate model is compared with alternative models based on a variational autoencoder or the principal component analysis using radial basis functions. Based on this comparison, the advantages of the proposed method are demonstrated.