A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
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气体动力学欧拉方程的三阶精确直接欧拉GRP格式
DOI：
10.1016/j.jcp.2014.01.041
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发表时间：
2014-05
影响因子：
4.1
通讯作者：
Tang Huazhong
中科院分区：
文献类型：
--
作者：
Wu Kailiang;Yang Zhicheng;Tang Huazhong
提出并实现了气体动力学中一维和二维（1D和2D）欧拉方程的三阶精确直接欧拉广义黎曼问题（GRP）格式。它是Ben-Artzi et al.(2006)[5]提出的二阶精确GRP方案的扩展。利用初始数据的高阶WENO重构、解在奇点处的时间导数的极限值和雅可比矩阵，导出了三阶精确GRP格式数值流场的近似状态。除了流体变量的一阶时间导数的极限值外，本GRP格式的发展还需要二阶时间导数，这是通过黎曼不变量和Rankine-Hugoniot跳跃条件这两个主要成分直接解析欧拉公式中的局部GRP得到的。不幸的是，对于出现跨音速稀疏波的声波情况，雅可比矩阵在声波线上是奇异的。为此，这些近似状态以一种不同的方式给出，这种方式是基于跨声速稀疏波的解析解析和局部二次多项式插值。二维GRP方案采用三阶精确时间分割方法实现。通过数值算例与二阶精确GRP格式进行比较，验证了该格式的准确性和有效性。
The paper proposes and implements a third-order accurate direct Eulerian generalized Riemann problem (GRP) scheme for one- and two-dimensional (1D & 2D) Euler equations in gas dynamics. It is an extension of the second-order accurate GRP scheme proposed in Ben-Artzi et al. (2006) [5]. The approximate states in numerical fluxes of the third-order accurate GRP scheme are derived by using the higher-order WENO reconstruction of the initial data, the limiting values of the time derivatives of the solutions at the singularity point, and the Jacobian matrix. Besides the limiting values of the first-order time derivatives of fluid variables, the second-order time derivatives are also needed in developing the present GRP scheme and obtained by directly and analytically resolving the local GRP in the Eulerian formulation via two main ingredients, i.e. the Riemann invariants and Rankine–Hugoniot jump conditions. Unfortunately, for the sonic case that the transonic rarefaction wave appears in the GRP, the Jacobian matrix is singular on the sonic line. To this end, those approximate states are given in a different way that is based on the analytical resolution of the transonic rarefaction wave and the local quadratic polynomial interpolation. The 2D GRP scheme is implemented by using the third-order accurate time-splitting method. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed GRP scheme, in comparison to the second-order accurate GRP scheme.
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可压缩流体流动的自适应 GRP 方案
影响因子：
4.1
作者：
Han, Ee;Li, Jiequan;Tang, Huazhong
通讯作者：
Tang, Huazhong
DOI：
10.1016/j.jcp.2013.02.018
发表时间：
2013-06
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Jian Zhao;Huazhong Tang
通讯作者：
Jian Zhao;Huazhong Tang
影响因子：
3.1
作者：
Liska, R;Wendroff, B
通讯作者：
Wendroff, B
影响因子：
2.9
作者：
Andrew T. Sornborger;E. Stewart
通讯作者：
Andrew T. Sornborger;E. Stewart
DOI：
10.1016/j.jcp.2011.07.004
发表时间：
2011
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Zhicheng Yang;Peng He;Huazhong Tang
通讯作者：
Zhicheng Yang;Peng He;Huazhong Tang