一类TVD型的迎风紧致差分格式

1.
中国空气动力研究与发展中心中国空气动力研究与发展中心,四川绵阳 621000;2.国家计算流体力学实验室国家计算流体力学实验室,北京 100083;3.防化研究院信息研究中心,北京 102205;4.同济大学软件学院,上海 200331

基金项目: 国家自然科学基金资助项目(1017201590205010)

A Class of Compact Upwind TVD Difference Schemes

1.
China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, P. R. China;

摘要: 给出一种迎风型TVD(total variation diminishing)格式的构造方法，该方法通过限制器来抑制线性紧致格式在模拟间断流场时的非物理波动，可构造出非线性TVD型紧致格式(CTVD)．然后采用该法构造出了3阶和5阶的TVD型紧致格式，并通过模拟一维组合波和Riemann问题，二维激波-涡相互干扰和激波-边界层相互作用等来考察它们的性能．数值实验表明了该类格式的高阶精度和分辨率，且过间断基本无振荡．
- 高精度计算格式 /
- 紧致格式 /
- TVD格式 /
- 激波-涡 /
- 激波-边界层
Abstract: A new method was proposed for constructing total variation diminishing(TVD)upwind schemes in conservation forms.Two limiters were used to prevent non-physical oscillations across discontinuity.Both limiters can ensure the nonlinear compact schemes TVD property.Two compact TVD(CTVD)schemes were tested,one is third-order accuracy,and the other is fifth-order.The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems,as well as a two-dimensional shock-vortex interaction and a shock-boundary flow interaction.Numerical results show their high-order accuracy and high resolution,and low oscillations across discontinuities.
- high-order scheme /
- compact scheme /
- TVD scheme /
- shock-vortex /
- shock-boundary

[1]	Lele S K. Compact finite difference schemes with spectral-like resolution[J].Journal of Computational Physics,1992,103(1):16—42. doi: 10.1016/0021-9991(92)90324-R
[2]	Ravichandran K S. Higher order KFVS algorithms using compact upwind difference operators[J].Journal of Computational Physics,1997,230(2):161—173.
[3]	Tadmor E. Convenient total variation diminishing conditions for nonlinear difference schemes[J].SIAM Journal on Numerical Analysis,1988,25(5):1002—1014. doi: 10.1137/0725057
[4]	Osher S. Riemann solvers, the entropy condition and difference approximations[J].SIAM Journal on Numerical Analysis,1984,21(2):217—238. doi: 10.1137/0721016
[5]	涂国华，袁湘江，陈陆军.适用于超声速的一种通量限制型紧致格式[J]. 航空学报,2004,25(4):327—332.
[6]	Pirozzoli S. Conservative hybrid compact-WENO schemes for shock-turbulence interaction[J].Journal of Computational Physics,2002,178(1):81—117. doi: 10.1006/jcph.2002.7021
[7]	Jiang G-S, Shu C-W. Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics,1996,126(1):202—228. doi: 10.1006/jcph.1996.0130