低Ma数预处理间断Galerkin算法  

Preconditioning discontinuous Galerkin method for low Mach number flows

作　　者：谭勤学[1] 任静[1] 蒋洪德[1] 

机构地区：[1]清华大学热能工程系,燃气轮机研究所,北京100084

出　　处：《清华大学学报（自然科学版）》2015年第1期134-140,共7页Journal of Tsinghua University(Science and Technology)

摘　　要：该文为研究间断Galerkin方法对低Ma数流动计算的实用性,将有限体积预处理矩阵方法引入间断Galerkin框架,针对低Ma数问题发展了三维粘性流动求解方法。行波算例(traveling wave)表明:在间断Galerkin框架下引入预处理矩阵方法可用于低Ma数粘性流动的计算,且能保持间断Galerkin方法原有的离散精度。顶盖驱动流动、层流边界层、后台阶湍流流动和方腔内自然对流4个经典算例,检验了预处理间断Galerkin方法求解低Ma数流动的可行性及程序的可靠性。不同Ma数绕NACA0012无粘流动算例进一步表明,该文所用预处理间断Galerkin方法计算收敛速度几乎与Ma数无关。The finite volume preconditioning method is applied to the discontinuous Galerkin method for three-dimensional viscid low Mach number flows. The traveling wave ease is used to verify that the preconditioning discontinuous Galerkin method is suitable for viscid low Mach number flows and that the method retains the original discrete accuracy of the discontinuous Galerkin method. The results for four classical cases （lid driven incompressible flow, a Blasius boundary layer, a backward facing step with turbulent flow and natural convection in a square enclosure） validate the applicability of the preconditioning discontinuous Galerkin method and the reliability of the program. The flow around a NACA0012 airfoil for three different Mach numbers show that the convergence speed is independent of the Mach number.

关 键 词：间断GALERKIN方法 预处理矩阵方法 低Ma数 无积分 矩阵运算 

分 类 号：O354[理学—流体力学]