用于三维非均质流场计算的改进流线迎风Petrov-Galerkin(SUPG)方法  

Modified Streamline Upwind Petrov-Galerkin(SUPG)Strategy for Calculation of Three-Dimensional Heterogeneous Flow Problems

作　　者：苏波[1] 韩向科[2] 

机构地区：[1]江苏大学土木工程与力学学院,江苏镇江212013 [2]中冶天工上海十三冶建设有限公司,上海200092

出　　处：《西安交通大学学报》2014年第3期128-134,共7页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金青年基金资助项目(51108210);江苏省博士后基金资助项目(1301048C);国家自然科学基金专项数学天元基金资助项目(11226308)

摘　　要：在流线迎风Petrov-Galerkin(SUPG)稳定有限元方法基础上,通过引入双时间步法和变量分裂算法,发展了一种可用于三维非均质流场计算的改进SUPG方法。该方法摒弃了传统不可压缩流动问题中密度为常数的假定,采用包含密度输运方程的流体运动控制方程;基于变量分裂算法,速度、压强场采用同阶插值函数进行空间离散,使改进SUPG方法具有简明的有限元格式,同时对速度场、压强场进行迭代求解,以降低线性代数方程组的阶数。双时间步法的引入,有利于提高SUPG方法对复杂非定常问题的求解效率。采用该方法对非均质、非定常三维矩形管道重力作用下的自由流动问题进行了分析,研究了重力作用下两种不同密度液体的相对运动过程。计算分析表明:在采用较大时间步的情况下,速度场和压强场在整个流动过程中随时间平稳过渡且分布光滑,没有出现数值波动现象;旋涡位置及其随时间变化的规律与经典文献结果相符,没有出现跳跃和不连续现象。算例分析表明,改进SUPG方法具有良好的计算精度及数值稳定性,可用于三维非均质流动类似问题的研究。By introducing the dual-time stepping method and the variable splitting algorithm, a modified SUPG strategy is developed based on the stable streamline upwind Petrov-Galerkin （SUPG） finite element method, where the traditional assumption of constant density for incompressible flow problem is abandoned and the density transportation equation is introduced into the governing equations. The velocity and pressure fields are discretized with interpolating function of the same order, thus finite element scheme of the modified SUPG strategy gets simple and clear, and the order of algebraic equations is reduced. The dual-time stepping method is also introduced to enhance calculation stability of the SUPG strategy for complex unsteady problems. A free flow with heterogeneous, unsteady field of three-dimensional rectangular pipe under gravity and the whole relative motion between two types of liquids with different density areanalyzed. The calculation results indicate that the velocity and pressure fields distribute and transmit smoothly with time and no numerical wave occurs in the case of greater time steps; the vortex position and its varying regulation coincide well with the results in the classic literatures without iumps and discontinuities. Example proves the numerical stability and accuracy of the modified SUPG method.

关 键 词：不可压流动 有限元法 分裂算法 流线迎风 

分 类 号：O357.1[理学—流体力学]