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将基函数法应用到不可压缩黏性流动的数值模拟中去,采用人工压缩性技术、通量分裂法及中心格式和迎风格式相结合的技术,构造出可数值求解三维不可压缩流体N-S方程的三角函数类型的基函数格式.为了验证此方法,首先计算了有限长度的圆管内流动,解出的速度分布和压力分布除入口段和出口段外,与泊肃叶流的结果十分吻合.在方法得到初步验证后,又采用三角函数基函数及非结构网格生成技术,进一步数值地研究了二维和三维情况下动脉瘤内的血液动力学问题,计算了定常情况下动脉瘤内的速度、压力和剪切力分布并研究了动脉瘤的几何形状对血液动力学的影响.
The basic function method is applied to the numerical simulation of incompressible viscous flow. The artificial compressibility technique, the flux splitting method and the combination of the central format and the windward format are used to construct the numerical solution of the three-dimensional incompressible fluid NS equations In order to validate this method, we firstly calculate the flow in a finite length tube, and the velocity distribution and pressure distribution are consistent with the results of Poiseuille flow except for the inlet and outlet sections. In After the initial validation of the method, the trigonometric function basis functions and unstructured grid generation techniques were used to further study the hemodynamic problems in aneurysms in two-dimensional and three-dimensional cases. The velocity in the aneurysm under normal conditions was calculated , Stress and shear distribution and study the hemodynamic effects of aneurysm geometry.