基于涡量-流函数法的曲面方腔顶盖驱动问题的数值研究  

Numerical Studies of Lid-driven Cavity Flows in Curved Surfaces Based on Vorticity-Stream Function Method

作　　者：陈玉竹 谢锡麟 CHEN Yuzhu;XIE Xilin(Department of Aeronautics and Astronautics,Fudan University,Shanghai 200433,China)

机构地区：[1]复旦大学航空航天系,上海200433

出　　处：《复旦学报（自然科学版）》2023年第2期137-147,共11页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金面上项目(11972120,11472082)。

摘　　要：对几种不同几何构型下的曲面方腔顶盖驱动问题进行了数值研究。采用曲面上的涡量-流函数方法和曲线坐标系下的有限差分格式对曲面上的不可压缩流动Navier-Stokes方程进行数值求解。计算结果表明:在Re=100和Re=1000下得到的稳态解与近期文献中基于原始变量的高阶曲面有限元方法所得的结果一致;在有限雷诺数下,正高斯曲率对漩涡有排斥作用,负高斯曲率对漩涡有吸引作用;曲面的曲率与涡量分布有复杂的耦合作用,可以造成更多漩涡结构的产生,且雷诺数越高,高斯曲率绝对值越大,几何效应越明显。Lid-driven cavity flows in curved surfaces with several types of geometric configurations have been investigated numerically.The surface vorticity-stream function method is used to solve the Navier-Stokes equations for incompressible flows in curved surfaces with the finite difference approach under curvilinear coordinates.The simulation results in Reynolds numbers of 100 and 1000 are consistent with the results obtained in the recent literature using the high-order surface finite element method based on the primitive variables.From the simulation results,we also observe that areas with positive Gaussian curvature tend to repulse vortices,and areas with negative Gaussian curvature tend to attract vortices under finite Reynolds numbers.The coupling effects between the surface curvature and vorticity distribution may cause more vortex structures to appear in the corners.The geometric effects increase with greater Reynolds numbers and greater Gaussian curvatures.

关 键 词：二维曲面流动 曲面不可压缩流动Navier-Stokes方程 涡量-流函数法 涡量动力学 

分 类 号：O35[理学—流体力学]