An Efficient Method for Density Projection Field Solution Based on Finite Element Method

In the wind tunnel flow field, the relationship between the density projection field, caused by disturbance, and the offset angle of light meets the Poisson equation. However, the source term of the Poisson equation is composed of a series of measured offset angles, which makes it can not be solved effectively by the existing methods. On the basis of the finite element method (FME), we established the fitting formula between the offset angles in the source terms and their corresponding coordinates by employing the Genetic algorithms and back-propagation (GA-BP) neural network. Meanwhile, when the element load vectors were solved, the double integral expression of the entire triangle element prediction was approximately replaced by the constant expression of the triangle vertex element prediction. Simulation experiments demonstrate that compared with the traditional interpolation, the neural network can achieve higher fitting precision. And the proposed algorithm greatly improves the operation speed under the same solution error. By applying the proposed algorithm to the real flow field, the obtained features of the density field are similar to those obtained in the real environment. These imply that the proposed method provides a new useful tool for the study of the density projection field.