一种通量加权型紧致格式

基金项目: 国家自然科学基金(1032100210672012)

A flux-weighted compact scheme

1.
China Aerodynamics Research and Development Center, Mianyang 621000, China
2.
National Computational Fluid Dynamics Laboratory, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
3.
School of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
4.
School of Jet Propulsion, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

摘要: 将通量加权的思想引入到紧致格式中,构造了一个传统方法与紧致格式混合组成的加权型差分格式.利用该格式与二阶TVD格式分别计算了一维方波、组合波问题和一些黎曼问题,如Sod问题和Shu问题,以及一维定常激波问题.计算结果的比较表明加权格式无论在捕捉各种间断,还是在分辨各种复杂波系上,都具有较大的优势,并与精确解非常吻合.
- 航空、航天推进系统 /
- 数值方法 /
- 迎风紧致格式 /
- 通量加权型差分格式
Abstract: With introduction of flux-weighted concept into the compact scheme,a new flux-weighted compact scheme was presented by combining classical scheme and compact scheme.This scheme and a 2nd-order total variation diminishing(TVD) scheme were used to calculate one-dimensional square waves,combine waves and some Riemann problems,such as Sod problem and Shu problem,as well as one-dimensional steady shock.The results show that the new scheme has advantage over the 2nd-order TVDscheme in capturing various discontinuities or resolving various complex waves.The results solved by the new scheme are also highly consistent with exact solutions.
- aerospace propulsion system /
- numerical method /
- upwind compact scheme /
- weighted essentially non-oscillatory(WENO) schemess

[1]	袁湘江,桂业伟.适于超音速流动的高精度高分辨度算法研究(阶段报告)[R].CARDC-20010015,2000.
[2]	Lele S K.Compact finite difference schemes with spectrailike resolution[J].J.Comput.Phys.,1992,103:16-42.
[3]	Harten A.High resolution schemes for conservation laws[J].J.Comp.Phys.,1983,49:357-393.
[4]	Harten A,Osher S.Uniformly high-order accurate non-oscillatory schemes I.[J].SIAM J.Numer.Anal.,1987,24:279-309.
[5]	傅德薰,马延文.群速度控制方法及三维平面混合流的数值模拟[C]//中国力学学会现代力学与科技进步学术大会论文集.北京:中国力学学会,1997:533-538.
[6]	袁湘江,周恒.高精度格式计算激波的新方法[J].应用力学与数学,2000,21(5):441-450.YUAN Xiangjiang,ZHOU Heng.Numerical schemes with high order of accuracy for the computation of shock waves[J].Applied Mathematics and Mechanics,2000,21(5):441-450.
[7]	Ravichandran K S.Higher order KFVS algorithms using compact upwind difference operators[J].J.Comp.Phys.,1983,49:357-393.
[8]	Liu X D,Osher S,Chen T.Weighted essentially non-oscillatory schemes[J].J.Comp.Phys.,1994,115:200-212.
[9]	周恒,袁湘江.关于NND格式的两点注记[J].空气动力学学报,2000,18(1):52-54.ZHOU Heng,YUAN Xiangjiang.Notes on the NND scheme[J].ACTA Aerodynamics Sinica,2000,18(1):52-54.