基于深度神经网络的高阶非线性激波判别式

In the numerical simulation of supersonic flow, accurately identifying shock wave position is essential to solve an aircraft's aerodynamic and thermal characteristics. The traditional artificial shock identification method seriously depends on empirical coefficients, which has some limitations in practical application. A higher-order nonlinear shock wave discriminant is constructed by using a deep neural network to establish a more general shock identification method. Based on the training data set and the test data set, the depth Feedforward Neural Network is constructed, and the model is trained to meet the prediction accuracy of shock wave identification; it is applied to one-dimensional Lax and Sod shock problems and two-dimensional supersonic inviscid circular cylinder to verify the accuracy of the discriminant. The results show that this paper's high-order nonlinear shock discriminant can more accurately distinguish the smooth region and shock region than the artificial shock discriminant. Secondly, the shock discriminant can accurately identify the shock position under different Mach numbers and grid distributions, but the accuracy of shock identification depends on the grid resolution.