The anisotropic graph neural network model with multiscale and nonlinear characteristic for turbulence simulation

The turbulent flow characteristics, such as its multiscale and nonlinear nature, make the solution to turbulent flow problems complex. To simplify these problems, traditional methods have employed simplifications, such as RANS and LES models for dealing with the multiscale aspect and linear approximation theories for dealing with the nonlinear aspect. We designed a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network with spatial convolutions and nonlinear fitting capabilities. Unlike traditional methods, this model computes turbulence data directly without resorting to simplified formulas. The multiscale problem is addressed by an anisotropic filter operator, and the nonlinear problem is dealt with through nonlinear correlation and nonlinear activation functions. To enhance the training efficiency of the model, a single training framework was implemented. This framework allows models trained on turbulent data with different Reynolds numbers to be applied. The relative errors for the X-axis velocity (U), Y-axis velocity (V) and pressure (P) are 0.932 %, 1.020 % and 0.594 %, respectively, when using turbulence data with the Reynolds number (Re) of 5×10⁵ as the training set. Using Re = 1 × 10³ and Re = 5 × 10⁵ as training data and Re = 1× 10⁵ as test data, the relative errors for U, V and P were found to be 2.527 %, 6.284 % and 0.799 % (Re = 1× 10⁵). The study also analysed the impact of the anisotropic filter operator and nonlinearity on turbulence simulation and found that both play a critical role in turbulence calculation. These experiments demonstrate that the multiscale nonlinear turbulence simulator has a high computational performance in turbulence calculation.