Complemental Standard Galerkin Finite Element Method In Fluid Mechanics And Its Application In Wind Field Around Buildings

In recent years,with the rapid development of computer technology and numerical method,numerical simulation,based on fluid mechanics theory,has become an important tool for wind analisys of long-span spatial structures,high-rise buildings and bridges.Emphasis is put on Complemental Standard Galerkin(CSG)finite element method in fluid dynamics in the paper.The AADS_Fluid module is developed and the wind field around buildings is simulated and studied,providing theoretical and technical support for the design of wind load.Firstly,the basic theory of fluid mechanics aresummarized and time integration method and finite element method are presented for discretizing the governing equations.The wave problems of finite element solution of one dimensional steady convection diffusion equation are analyzed and the CSG finite element method is proposed,including the formation of exponential function based shape function,the compensation term for the discontinuity of the function.Compared with the liner Lagrange interpolation function finite element method and analytical solution,CSG finite element method is accurate and effective to deal with the problem of numerical wave.Secondly,based on the results of one-dimensional problem,CSG finite element method is used to solve N-S equations.The whole process includes derivation of two-dimensional and three dimensional EFBI(exponential function based interpolation)function,the compensation for the discontinuity of the first derivative of the function between elements and the non-conservative flux of mass,momentum and energy between adjacent elements,the time integration method and the split method for N-S equations.The solving technique and algorithm mainly based on ? method and implemented in the AADS_Fluid module.The chosen examples show that the pressure and velocity values calculated by CSG method and ANSYS_Fluent have good agreement,indicating that CSG is accurate and feasible,and it is an independent method of SUPG and CBS method.Finally,based on research of the finite element method for fluid mechanics,a comprehensive method including CSG finite element method,similarity theory in fluid dynamics,formation of computational wind field and compactly supported radial basis function method for data transfer is developed for calculation of pressure coefficient on the building in wind field.Compared with experiment,the method has the characteristics of reliability,less calculation and accuracy.This method is applied to further research on CAARC standard tall building model,to analyze under different surface roughness of the terrains,different wind angles and with hole in the buildings,the change of pressure coefficients on the buildings,the influence of surrounding buildings on the wind field,as well as shear force and skin friction drag,providing a reference for engineering practice.