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使用两步四阶GRP格式对二维黎曼问题的数值模拟
发表时间：2017-04-14 浏览量：3441 下载量：649
| 全部作者： | 杜知方，李杰权 |
| 作者单位： | 北京师范大学数学科学学院 |
| 摘 要： | 提出对守恒律方程组的两步四阶时间离散方法，并构造两步四阶广义黎曼问题（generalized Riemann problem，GRP）格式。新的格式易于实现，相比其他高阶格式计算开销小，在计算中表现出对流场的高分辨率。欧拉方程组的二维黎曼问题是流体力学研究中的一个基础性课题，其中蕴含了很多流体现象，包括激波反射、涡的生成和滑移面的不稳定性等。首先介绍两步四阶GRP格式的构造，随后通过对典型二维黎曼问题的计算并与二阶GRP格式对比，展示新的格式在二维可压缩流计算方面的性能。结果表明，两步四阶格式不仅能清晰分辨解的基本结构，同时与二阶格式相比，分辨滑移面上的小尺度结构具有明显优势。 |
| 关 键 词： | 计算数学；二维黎曼问题；两步四阶格式；广义黎曼问题解法器；Lax-Wendroff方法 |
| Title： | Numerical simulation of two-dimensional Riemann problems with the two-stage fourth-order GRP scheme |
| Author： | DU Zhifang, LI Jiequan |
| Organization： | School of Mathematical Sciences, Beijing Normal University |
| Abstract： | In this paper, we have proposed a newly developed two-stage fourth-order time discretization for the hyperbolic conservation laws. In addition, a two-stage fourth-order generalized Riemann problem (GRP) scheme was constructed based on it. The newly developed scheme is easy to implement and requires less computational cost compared with other high-order schemes. It shows excellent resolution in the numerical computations. Two-dimensional Riemann problems of the Euler equations are fundamental in the study of the fluid dynamics. Their solutions reveal a lot of fluid phenomena such as Mach reflections, spiral formations, interface instabilities and so on. In this paper, we will firstly review the construction of the two-stage fourth-order GRP scheme in detail. Then we will show the performance of the new scheme to resolve the two-dimensional compressible flow by taking it to the simulation of the several classical two-dimensional Riemann problems and compare it with the classical second-order GRP scheme. Results indicate that the new two-stage fourth-order scheme can provide an excellent resolution for the basic structure of the solution. Compared with the second-order scheme, it can also have a great advantage to capture many small-scaled structures along the slip lines. |
| Key words： | computational mathematics; two-dimensional Riemann problem; two-stage fourth-order scheme; generalized Riemann problem solver; Lax-Wendroff method |
| 发表期数： | 2017年4月第7期 |
| 引用格式： | 杜知方，李杰权. 使用两步四阶GRP格式对二维黎曼问题的数值模拟[J]. 中国科技论文在线精品论文，2017，10（7）：696-708. |
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