低Ma数预处理间断有限元方法研究
首发时间:2013-01-16
摘要:间断有限元方法是近年来发展起来的一种高精度数值计算方法。本文在高精度间断有限元方法的基础上,发展了一种全矩阵无积分过程的间断有限元实现方法,并结合预处理方法,针对低Ma数问题发展了三维粘性流动求解方法。通过前台阶超音速流动,顶盖驱动流动,层流边界层,绕NACA0012翼型流动,验证了预处理间断有限元方法求解低Ma数问题的可行性及程序的可靠性。绕NACA0012翼型扰流问题的计算结果进一步表明,在Ma>0.001时预处理的间断有限元方法能较好收敛,且收敛速度几乎与Ma无关。
关键词: 间断有限元 预处理方法 低Ma数 无积分, 矩阵运算
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Precondition Discontinuous Galerkin Method For Viscid Low Mach Number Flow
Abstract:The discontinuous galerkin methods have recently become popular for the solution of systems of conservation laws to arbitrary order of accuracy. In this paper, we present preconditioning technique for viscid low Mach number flows. A discontinuous galerkin only include matrix operation formulation that avoids the use of discrete quadrature formulas is described. Four classical problems were used to verify the code, including the forward facing step problem, the Lid Driven flow problem, the Blasius boundary layer, the flow around NACA0012 airfoil. The results show the presented preconditioning techniques can be used for viscid low mach numbers flow's high order simulation. By using this precondition discontinuous galerkin methods, the convergence for the flow around NACA0012 airfoil problem is quite well and it is independent on the Mach number, when the Mach number is higher than 0.001.
Keywords: Discontinuous Galerkin Method, Precondition Method, Low Ma Number, Quadrature Free, Matrix Operation
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