| 引用本文: | 王文龙,李桦,刘枫,等.基于TVD思想的高阶迎风紧致格式.[J].国防科技大学学报,2013,35(6):9-14.[点击复制] |
| WANG Wenlong,LI Hua,LIU Feng,et al.High order upwind compact schemes based on TVD algorithm[J].Journal of National University of Defense Technology,2013,35(6):9-14[点击复制] |
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| 基于TVD思想的高阶迎风紧致格式 |
| 王文龙, 李桦, 刘枫, 田正雨 |
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(国防科技大学 航天科学与工程学院， 湖南 长沙 410073)
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| 摘要: |
| 紧致格式具有模板紧凑、精度高的特点，然而直接应用该格式捕捉激波会产生虚假振荡。解决该问题有多种思路，本文着重研究基于TVD思想的紧致方法。推导了两种5阶迎风紧致格式，并采用Fourier分析比较其耗散与色散特性。采用保单调保精度方法和限制器两种不同的TVD方法，进行算例验证。计算结果表明，应用TVD方法后，格式对激波、接触间断分辨率好且鲁棒性增强，但不同的TVD方法仍存在精度降低、耗散不足等问题。 |
| 关键词: 紧致格式 激波捕捉 TVD方法 |
| DOI： |
| 投稿日期：2013-04-30 |
| 基金项目:国家自然科学基金资助项目（91016010，91216117） |
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| High order upwind compact schemes based on TVD algorithm |
| WANG Wenlong, LI Hua, LIU Feng, TIAN Zhengyu |
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(College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China)
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| Abstract: |
| Using the same stencils, the compact schemes can get higher accuracy and resolution compared with the traditional ones. But it will bring about spurious oscillations if the compact schemes are used directly. There are several methods to settle this problem. The TVD algorithm was selected in our study. Firstly, two five-order upwind compact schemes were introduced and Fourier analysis was used to compare their dissipation and dispersion characteristics. Secondly, two different TVD methods were applied to Euler equations. The performance of the numerical algorithm was assessed by performing preliminary simulations on some problems, such as the oblique shock reflection problem. The algorithm applied here is proven to have good resolution properties and robust of capturing shock waves and contacts, but it still has the problems of accuracy degree and lack of dissipation. |
| Keywords: compact scheme shock capture TVD algorithm |
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