The theoretical research of basic function method in incompressible viscous flow and its simulations in three-dimensional aneurysms  

作　　者：SHEN Fang1 & WU WangYi2 1 State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190, China 2 State Key Laboratory of Turbulence and Complex Systems & Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2009年第6期909-918,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：Supported by the National Natural Foundation of China (Grant Nos.40874077,40504020,and 40536029);the National Basic Research Program of China (Grant No.2006CB806304)

摘　　要：Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two-and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two- and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.

关 键 词：basic function UNSTRUCTURED grid ANEURYSM VISCOUS INCOMPRESSIBLE flow artificial COMPRESSIBILITY flux splitting 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]