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中文摘要：
为了增加间断Galerkin（Discontinuous Galerkin,DG）方法在非定常流动中的求解效率,本文开展了非定常流动的隐式DG方法研究。隐式DG方法的构造采用二阶向后差分格式（BDF2）进行时间项离散,非线性代数系统的求解基于Newton迭代法,采用块对称Gauss-Seidel（SGS）迭代法对线性方程组进行了求解。基于所发展的非定常流动的隐式DG方法,分别对等熵圆柱扰流和卡门涡街（Re=100）现象进行了数值模拟。研究结果表明,所发展的隐式DG方法能够达到设计精度,能够在高出显式方法两个数量级的时间步长上保持稳定,具有高的求解效率,且计算结果与显式方法和相关文献均吻合较好。
英文摘要：
An implicit discontinuous Galerkin method（DG） was investigated in order to increase the solving efficiency of unsteady flow.A second-order backward difference formulation（BDF2） was applied for the time-discretization.The Newton-Raphson method and block symmetric Gauss-Seidel（SGS） iteration were considered to solve non-linear equations and linear equations respectively.The isentropic flow around the cylinder and the Karmann vortex street phenomenon were simulated to verify the validity of the implicit DG method developed in the paper.The results show that the calculation accuracy of the implicit DG method can match designed accuracy.The solution using the implicit DG method keeps stable even the time step adopted is more than 100 times of that it has in the explicit method,with the favorable solving efficiency achieved,and the corresponding results are in good agreement with the explicit method and related references.
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