Study On Adaptive Wavelet Collocation Method For Transient Flow In Liquid Pipelines

The transient flow of liquid pipeline,whose equations are quasilinear hyperbolic partial differential equations,is very common in the process of petroleum transportation.The properties of that usually cause discontinuous solutions.In order to accurately simulate the change of the step,the general fixed uniform mesh needs to configure much more dense nodes in the pipeline,which may lead to heavy computation cost.Adaptive wavelet collocation method is developed on the basis of wavelet numerical technique.The capability of capturing local features and adaptive mesh,is suitable for solving problems with discontinuous solution.In this paper,the inherent features of the adaptive wavelet collocation points,as well as the influence of the wavelet threshold,the boundary extension method and wavelet resolution on the calculation precision and the compression performance is discussed.Based on the comparison of the fixed grid and the adaptive wavelet collocation method,the transient flow both in simple pipeline and complex pipeline is analyzed.The results show that the adaptive wavelet collocation method has good compression performance.When the mesh spacing decreases,the total number of points needed by adaptive wavelet collocation method tends to be stable.Compared with the general method,the adaptive wavelet collocation method can accurately simulate the transient flow in liquid pipeline,tracking the wave propagation effectively,generating dynamic adaptive grid,and reducing the number of grid points.