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| Developing shock-capturing difference methods | |
| 引用本文： | 涂国华,袁湘江,陆利篷. Developing shock-capturing difference methods[J]. 应用数学和力学(英文版), 2007, 28(4): 477-486. DOI: 10.1007/s 10483-007-0408-z |
| 作者姓名： | 涂国华 袁湘江 陆利篷 |
| 作者单位： | China Aerodynamics Research and Development Center Mianyang 621000，Sichuan Province，P. R. China Tianjin Key Laboratory of Modern Engineering Mechanics，Tianjin 300072，P. R. China National CFD Laboratory，Beihang University，Beijing 100083，P. R. China，China Aerodynamics Research and Development Center，Mianyang 621000，Sichuan Province，P. R. China National CFD Laboratory，Beihang University，Beijing 100083，P. R. China，School of Jet Propulsion，Beihang University，Beijing 100083，P. R. China |
| 摘 要： | A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions are carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes are converted into conservative forms, and the oscillation-free shock-capturing schemes are acquired. Two explicit upwind schemes (2nd-order and 3rd-order) and three compact upwind schemes (3rd-order, 5th-order and 7th-order) are modified by the method for hyperbolic systems and the modified schemes are checked on several one-dimensional and two-dimensional test cases. Some numerical solutions of the schemes are compared with those of a WENO scheme and a MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly. |
| 关 键 词： | 激波捕捉 差分法 高阶格式 高分辨率 逆风格式 |
| 收稿时间： | 2006-02-24 |
| 修稿时间： | 2007-01-27 |
Developing shock-capturing difference methods |
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| Tu Guo-hua,Yuan Xiang-jiang,Lu Li-peng. Developing shock-capturing difference methods[J]. Applied Mathematics and Mechanics(English Edition), 2007, 28(4): 477-486. DOI: 10.1007/s 10483-007-0408-z | |
| Authors: | Tu Guo-hua Yuan Xiang-jiang Lu Li-peng |
| Affiliation: | 1. China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan Province, P. R. China;Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin 300072, P. R. China;National CFD Laboratory, Beihang University, Beijing 100083, P. R. China 2. China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan Province, P. R. China;National CFD Laboratory, Beihang University, Beijing 100083, P. R. China 3. School of Jet Propulsion, Beihang University, Beijing 100083, P. R. China |
| Abstract: | A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions are carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes are converted into conservative forms, and the oscillation-free shock-capturing schemes are acquired. Two explicit upwind schemes (2nd-order and 3rd-order) and three compact upwind schemes (3rd-order, 5th-order and 7th-order) are modified by the method for hyperbolic systems and the modified schemes are checked on several one-dimensional and two-dimensional test cases. Some numerical solutions of the schemes are compared with those of a WENO scheme and a MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly. |
| Keywords: | high order scheme shock-capturing upwind scheme compact scheme high resolution conservative scheme |
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