高精度多维限制器的性能分析

孙迪; 阎超; 于剑; 屈峰; 华俊

doi:10.13700/j.bh.1001-5965.2014.0185

高精度多维限制器的性能分析

doi: 10.13700/j.bh.1001-5965.2014.0185

北京航空航天大学航空科学与工程学院, 北京 100191

基金项目: 国家973计划资助项目(2009CB724104)

详细信息

作者简介:
孙迪(1991—),女,安徽巢湖人,博士生,sundi@ase.buaa.edu.cn

通讯作者:
阎超(1963—),男,江苏徐州人,教授,yanchao@buaa.edu.cn,主要研究方向为计算空气动力学.

中图分类号: V123.4
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出版历程
- 收稿日期: 2014-04-08
- 网络出版日期: 2015-03-20

Performance analysis of high accuracy multi-dimensional limiting process

School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 目前常用的限制器大都是基于一维构造,无法在多维情况下保证物理量的单调特性进而导致非物理振荡.为弥补传统方法的这一构造缺陷,多维限制器(MLP)通过多维修正使单元通量值介于周围相邻单元通量的最大值和最小值之间,在保证求解精度的情况下有效避免了多维振荡.基于一维激波管、无黏涡及激波边界层干扰等算例,对高精度MLP的特性进行了研究分析.结果显示:3阶MLP在连续和间断区域均可有效地避免多维振荡;与高阶WENO(Weighted Essentially Non-Oscillatory)方法相比,3阶MLP不仅算法简单、易于实现,还可显著提高求解的精度、保单调性及收敛性.因此可用于工程及科学研究的复杂流动,具有较好的应用前景.
- 高精度多维限制器 /
- 多维限制器 /
- 保单调性 /
- 激波边界层干扰 /
- WENO格式
Abstract: The conventional limiting process is mostly based on one-dimensional structure, which cannot keep monotonic features of quantities under conditions of multi-dimensional discontinuities, leading to non-physical oscillations. In order to overcome the structure defects of the conventional methods, multi-dimensional limiting process (MLP) is a high accuracy limiter whose basic idea is that the vertex values interpolated at a grid point should be within the maximum and minimum cell-average values of neighboring cells through multi-dimensional correction. The major advantage of MLP is to avoid multi-dimensional oscillatory effectively and ensure solving accuracy. According to a set of test cases including one-dimensional shock tube, non-viscous vortex flow and shock boundary-layer interaction, the performance of MLP with high accuracy was analyzed, it is verified that third-order MLP can avoid multi-dimensional oscillatory effectively both in continuous and discontinuous area. Compared with higher-order WENO (weighted essentially non-oscillatory) schemes, the third-order MLP maintains several desirable characteristics, such as simple algorithm, simple implementation, improving the solving accuracy, monotonicity and convergence. For these properties, MLP can be applied to study complicated flow in engineering and scientific research, and is expected to have a bright application future.
- high accuracy multi-dimensional limiting process /
- multi-dimensional limiting process /
- monotonicity /
- shock boundary-layer interaction /
- WENO schemes

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