二维非定常Navier-Stokes方程精确的对偶变分原理族  

EXACT DUAL VARIATIONAL PRINCIPLES FOR 2-D UNSTEADY NAVIER-STOKES EQUATIONS

作　　者：刘高联[1] 

机构地区：[1]上海大学力学所,上海200072

出　　处：《工程热物理学报》2007年第6期929-932,共4页Journal of Engineering Thermophysics

基　　金：国家自然科学基金(Grant No.50136030);上海市重点项目基金(Project No.y0103)资助

摘　　要：本文采用基于待定函数的系统反推法首次成功地导出了二维非定常粘性流动Navier-Stokes方程的精确变分原理,并进而应用轮转变换导出其对偶变分原理,从而为粘流,特别是湍流的直接数值模拟(通过有限元法或变分差分解法等)或求近似解析解奠定了重要的和严密的理论基础.By means of a systematic reversed-deduction approach incorporating method of undetermined function a mixed variational principle （VP） for 2-D unsteady Navier-Stokes equations is generated for the first time. Then its dual VP is also established via the Friedrichs＇ involutory transformation. Thus a new rigorous theoretical foundation for the numerical/approximate-analytical solution of viscous flow, especially for the direct numerical simulation of turbulent flow, is founded.

关 键 词：粘性流动 NAVIER-STOKES方程 变分原理 有限元法 

分 类 号：V21[航空宇航科学与技术—航空宇航推进理论与工程]