无自由参数型混合格式

doi:10.13700/j.bh.1001-5965.2014.0134

北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (2): 318-322.doi: 10.13700/j.bh.1001-5965.2014.0134

无自由参数型混合格式

王来, 吴颂平

北京航空航天大学航空科学与工程学院, 北京 100191

收稿日期:2014-03-20 出版日期:2015-02-20 发布日期:2015-03-12
通讯作者: 吴颂平(1955—), 男, 天津人, 教授, wusping825@163.com, 主要研究方向为高超声速化学非平衡流、可压缩流数值模拟、有限元方法等. E-mail:wusping825@163.com
作者简介:王来(1991—), 男, 湖北潜江人, 硕士生, wanglaideyx@163.com
基金资助:
NSFC重大研究计划重点项目(91016006)

Hybrid finite difference schemes without free parameters

WANG Lai, WU Songping

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

Received:2014-03-20 Online:2015-02-20 Published:2015-03-12

摘要/Abstract

摘要：

针对紧致-加权本质无振荡混合格式中子格式的权重,设计了新的算子.该算子利用模板的光滑因子求解权重,避免引入自由参数,提高了格式的易用性和鲁棒性.利用新的权重算子,分别将两种五阶迎风紧致格式与WENO-Z(Weighted Essentially Non-Oscillatory Scheme)耦合.新权重算子使子格式之间的切换较为光滑.WENO-Z能够保持格式在极点附近的精度,紧致格式在光滑区域耗散低,混合格式因此能够保持高分辨率、高精度特性以及对间断的捕捉能力.数值试验针对若干双曲型方程算例展开,比较了两种混合格式在采用新权重算子与采用其他典型算子时的数值特性.结果表明无自由参数型权重算子性能良好.

关键词: 混合格式, 无自由参数, 权重算子, 高分辨率, 低耗散

Abstract:

A new algorithm was proposed to calculate the weights of sub-schemes in hybrid compact-WENO (weighted essentially non-oscillatory) schemes. It used smoothness indicators of the stencils of hybrid schemes as variables to work globally. The new weight algorithm employed none freely user-defined parameter, making the hybrid schemes more robust and applicable. Two different 5th order upwind compact schemes were coupled with a 5th order WENO-Z scheme respectively. The new algorithm maked the transition between two sub-schemes more smoothly. Generally, WENO-Z could preserve the accuracy at critical points while compact schemes were less dissipative in smooth area. Thus, these hybrid schemes with new algorithm maintained high resolution and high order of accuracy qualities and shock-capturing abilities. Numerical tests were taken upon benchmarks of hyperbolic equations to test performances of these two hybrid schemes between the new weight algorithm and a typical one. Numerical results demonstrate that the new parameter-free weight algorithm performs well.

Key words: hybrid scheme, no free parameters, weight algorithm, high resolution, low dissipation

中图分类号:

V211.3

王来, 吴颂平. 无自由参数型混合格式[J]. 北京航空航天大学学报, 2015, 41(2): 318-322.

WANG Lai, WU Songping. Hybrid finite difference schemes without free parameters[J]. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2015, 41(2): 318-322.

参考文献

[1] Wang Z J, Fidkowski K,Abgrall R,et al.High-order CFD methods:current status and perspective[J].Interntional Journal for Numerical Methods in Fluids,2012,72(8):811-845.
[2] 阎超,于剑, 徐晶磊,等.CFD模拟方法的发展成就与展望[J].力学进展,2011,41(5):562-589. Yan C,Yu J,Xu J L,et al.On the achievements and prospects for the methods of the computational fluid dynamics[J].Advances in Mechanics,2011,41(5):562-589(in Chinese).
[3] Harten A,Osher S. Uniformaly high order accurate essentially nonoscillatory scheme,Ⅲ[J].Journal of Computational Physics,1987,71(2):231-303.
[4] Shu C W, Osher S.Efficient implementation of essentially non-oscillatory shock-capturing schemes[J].Journal of Computational Physics,1988,77(2):439-471.
[5] Borges R, Carmona M,Costa B,et al.An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J].Journal of Computational Physics,2008,227(6):3191- 3211.
[6] Henrick A K, Aslam T D,Powers J M.Mapped weighted essentially non-oscillatory schemes:achieving optimal order near critical points[J].Journal of Computational Physics,2005,207(2):542-567.
[7] Castro M, Costa B,Don W S.High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws[J].Journal of Computational Physics,2011,230(5):1766-1792
[8] Lele S K. Compact finite difference schemes with spectral-like resolution[J].Journal of Computational Physics,1992,103(1):16-42.
[9] Liu X L, Zhang S H, Zhang H X,et al.A new class of central compact schemes with spectral-like resolution Ⅰ :linear schemes[J].Journal of Computational Physics,248(1):235-256.
[10] Adams N A, Shariff K.A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems[J].Journal of Computational Physics,1996,127(1):27-51.
[11] Pirozzoli S. Conservative hybrid compact-WENO schemes for shock-turbulence interaction[J].Journal of Computational Physics,2002,178(1):81-117.
[12] Ren Y X, Liu M E,Zhang H X.A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws[J]. Journal of Computational Physics,2003,192(2)：365-386.
[13] Yu J, Yan C,Jiang Z H.A high resolution low dissipation hybrid scheme for compressible flows[J].Chinese Journal of Aeronautics,2011,24(4):417-424.
[14] 武从海,赵宁, 田琳琳.一种改进的紧致WENO混合格式[J].空气动力学报,2013,31(4):477-481. Wu C H,Zhao N,Tian L L.An improved hybrid cmpact-WENO scheme[J].Acta Aero Dynamica Sinica,2013,31(4):417-481(in Chinese).
[15] Shen Y Q, Zha G C.Generalized finite compact difference scheme for shock/complex flowfield interaction[J].Journal of Computational Physics,2011,230(12):4419-4436.

无自由参数型混合格式

Hybrid finite difference schemes without free parameters

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

编辑推荐

Metrics

本文评价

[1]	丁一帆, 尤红建, 张浩, 陈双军, 许斌, 孙韬. 面向高分辨率遥感影像的地形辐射校正方法[J]. 北京航空航天大学学报, 2018, 44(1): 27-35.
[2]	徐维铮, 孔祥韶, 郑成, 吴卫国. 一种三阶WENO-Z格式改进方法[J]. 北京航空航天大学学报, 2017, 43(12): 2400-2405.
[3]	董海涛, 刘福军, 韩冲. 守恒律方程的导数人工压缩法[J]. 北京航空航天大学学报, 2012, (7): 966-970.
[4]	杨中洲,李椿萱. 模拟可压缩流的高分辨率有限元法[J]. 北京航空航天大学学报, 2008, 34(02): 171-174.
[5]	白霞, 孙进平, 高飞. 0.1m分辨率机载SAR孔径依赖性运动补偿方法[J]. 北京航空航天大学学报, 2007, 33(08): 898-901.
[6]	王鹏波, 周荫清, 陈杰, 李春升. 高分辨率多通道天线星载SAR的MCCS成像算法[J]. 北京航空航天大学学报, 2006, 32(04): 440-444.
[7]	梁维斌, 李春升, 周荫清. 基于多通道天线高分辨率星载SAR 实现方法研究[J]. 北京航空航天大学学报, 2004, 30(09): 826-830.
[8]	王毛路, 李少洪, 毛士艺. 证据理论和神经网络结合的目标识别方法[J]. 北京航空航天大学学报, 2002, 28(5): 536-539.
[9]	王毛路, 李少洪, 毛士艺. 神经网络与D-S理论结合的HRR识别研究[J]. 北京航空航天大学学报, 2002, 28(4): 443-446.