非定常流动的隐式间断Galerkin方法研究

发布时间：2018-06-15 00:02

本文选题：间断Galerkin方法 + 隐式方法　；参考：《工程热物理学报》2017年04期

【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。
[Abstract]:In order to increase the efficiency of the discontinuous Galerkin (DG) method in solving unsteady flows, the implicit DG method for unsteady flows is studied in this paper. The implicit DG method is constructed by the second order backward difference scheme (BDF2). The solution of nonlinear algebraic systems is based on Newton iterative method. The block symmetric Gauss-Seidel-SGS iterative method is used to solve the linear equations. Based on the developed implicit DG method for unsteady flow, the phenomena of isentropic cylindrical turbulence and Carmen vortex are numerically simulated. The research results show that the developed implicit DG method can achieve the design accuracy, can maintain stability in two orders of magnitude time step of the explicit method, and has a high efficiency. The calculated results are in good agreement with the explicit method and related literature.
【作者单位】：西北工业大学动力与能源学院;
【基金】：国家自然科学基金项目(No.51576163;No.51236006)
【分类号】：O241.82

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