Maxwell流体不可压缩流动稳定性的多尺度分析与数值模拟  

Multiscale Analysis and Numerical Simulations for Stability of Incompressible Flow of Maxwell Fluid

作　　者：张玲[1] 欧阳洁[1] 郑素佩[1] 张红平[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《工程数学学报》2009年第3期480-488,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金重大项目(10590353);陕西省自然科学基金(2005A16)

摘　　要：本文对Maxwell流体小尺度不可压缩周期流,通过多尺度分析获得控制扰动流的大尺度均场方程和紧凑形式的四阶有效张量。对稳态平行流,通过对均场方程中均匀化算子的特征值进行理论分析,得到控制大尺度扰动流稳定性的临界粘性系数。然后对不同参数和初始条件,采用基于同位网格改进的SIMPLEC算法对均场方程和大尺度扰动流控制方程进行数值模拟,验证了多尺度理论预测的正确性,从而说明了本文所用多尺度分析方法和数值算法的有效性和可靠性。For the incompressible small-scale periodic flow of a Maxwell fluid, the mean-field equations which govern the transport of large-scale perturbations were obtained by the multiscale analysis. A general mathematical formalism was developed to determine the effective tensor. In general, the effective tensor is a fourth-order tensor, for which a compact representation was provided. The exact explicit expressions of the effective tensor were given for the parallel time-independent flow. For the Kolmogorov flow, the critical value of viscosity for stabilities of large scale perturbations was obtained by theoretical analyses of the eigenvalues of the homogenized operator in the mean-field equations. Then, the mean-field equations and the original linearized equations with respect to different parameters and initial conditions were simulated by using the modified SIMPLEC （Semi-Implicit Method for Pressure Linked Equations, Consistent） algorithm in the collocated grid system. The comparisons between the direct numerical simulations and the multiscale theoretic predictions demonstrated that the multiscale analysis and the numerical algorithm are effective and credible.

关 键 词：MAXWELL流体 稳定性 多尺度分析 均场方程 SIMPLEC算法 

分 类 号：O241.82[理学—计算数学] O357.1[理学—数学]