| 引用本文: | 范进之,李桦.高精度有限体积法与间断有限元法的比较.[J].国防科技大学学报,2014,36(5):33-38.[点击复制] |
| FAN Jinzhi,LI Hua.Comparison of high-precision finite volume method and discontinuous Galerkin method[J].Journal of National University of Defense Technology,2014,36(5):33-38[点击复制] |
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| 高精度有限体积法与间断有限元法的比较 |
| 范进之, 李桦 |
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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: |
| 通过数值算例，比较了高精度有限体积法和间断有限元法在求解不同问题时的表现。研究发现：在精度相同的条件下，间断有限元法的计算误差要明显小于有限体积法；间断有限元法的重构过程与高精度有限体积法相比较为简单，但高阶情形下解多项式的自由度较多并且需要计算体积分，因此整个求解时间较长。降低时间积分时解多项式的自由度数目是实现高精度算法在实际问题中应用的重要手段。 |
| 关键词: 高精度格式 有限体积法 间断有限元法 |
| DOI：10.11887/j.cn.201405006 |
| 投稿日期：2014-03-11 |
| 基金项目:中国航天科技集团公司航天科技创新基金资助项目 （CALT-16） |
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| Comparison of high-precision finite volume method and discontinuous Galerkin method |
| FAN Jinzhi, LI Hua |
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(College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China)
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| Abstract: |
| The high-precision finite volume method (FVM) and discontinuous Galerkin method (DGM) were compared in different test cases through numerical examples. Results show that:with the same precision, the calculation error of DGM is obviously less than that of FVM; DGM's reconstruction process is comparatively simpler than FVM's, but its computational time is much longer since its freedom-degree of polynomial solution is higher under the condition of high order and it needs to calculate volume points. Decreasing the freedom-degree numbers of polynomial solution in the time evolution process is an essential method for high-precision calculation in the reality applications. |
| Keywords: high-precision schemes finite volume method discontinuous Galerkin method |
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