An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids
An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids
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DOI：
10.4208/cicp.091113.280714a
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发表时间：
2014-12
影响因子：
3.7
通讯作者：
Laiping Zhang;Ming Li;W. Liu;Xin He
中科院分区：
文献类型：
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作者：
Laiping Zhang;Ming Li;W. Liu;Xin He
采用任意网格下的DG/FV混合格式，建立了求解二维Euler方程和Navier-Stokes方程的牛顿/LU-SGS(下-上对称Gauss-Seidel)迭代隐式方法。用牛顿迭代法求解非线性方程组，用LU-SGS迭代法解线性方程组。研究了隐式格式中CFL数、牛顿子迭代步数、雅可比矩阵更新频率等参数对收敛历史的影响。对几种典型的测试用例进行了仿真，并与传统的显式Runge-Kutta(RK)方案进行了比较。首先对Couette流进行了测试，以验证所提出的DG/FV混合格式的精度。在此基础上，对亚音速无粘绕流进行了数值模拟，并研究了参数对绕流的影响。最后，应用隐式算法模拟了亚音速圆柱绕流和方腔内的粘性绕流。数值结果表明，该隐式格式能有效地加快收敛速度。选择合适的参数可以提高隐式格式的效率。此外，在相同的框架下，DG/FV混合格式比同阶DG格式更有效。
A Newton/LU-SGS (lower-upper symmetric Gauss-Seidel) iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids. The Newton iteration was employed to solve the nonlinear system, while the linear system was solved with LU-SGS iteration. The effect of several parameters in the implicit scheme, such as the CFL number, the Newton sub-iteration steps, and the update frequency of Jacobian matrix, was investigated to evaluate the performance of convergence history. Several typical test cases were simulated, and compared with the traditional explicit Runge-Kutta (RK) scheme. Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes. Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also. Finally, the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity. The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently. Choosing proper parameters would improve the efficiency of the implicit scheme. Moreover, in the same framework, the DG/FV hybrid schemes are more efficient than the same order DG schemes.