| 引用本文: | 徐丹,王东方,陈亚铭,等.高精度有限体积格式在三维曲线坐标系下的应用.[J].国防科技大学学报,2016,38(2):56-60.[点击复制] |
| XU Dan,WANG Dongfang,CHEN Yaming,et al.High-order finite volume schemes in three-dimensional curvilinear coordinate system[J].Journal of National University of Defense Technology,2016,38(2):56-60[点击复制] |
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| 高精度有限体积格式在三维曲线坐标系下的应用 |
| 徐丹1, 王东方1, 陈亚铭2, 邓小刚1 |
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(1.国防科技大学 航天科学与工程学院， 湖南 长沙 410073;2.国防科技大学 理学院， 湖南 长沙 410073)
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| 摘要: |
| 为了构造在光滑区具有较高分辨率并且可以无振荡捕捉激波的高精度有限体积格式，同时降低格式在模板选择上遇到的困难，基于逐维重构方法，发展了结构网格下的高精度有限体积格式，并将这一格式推广到三维曲线坐标系下，从而可以适应相对复杂外形下的计算。为充分验证格式的有效性，选取一系列典型算例进行计算：在等熵涡输运和二维喷管流动中验证了格式的精度可以达到设计精度；在双马赫反射问题中格式也表现出良好的捕捉激波的能力。数值计算表明，上述格式在曲线网格上具有较高的数值精度和鲁棒的激波捕捉能力，适用于流体力学方程的计算。 |
| 关键词: 有限体积方法 高精度格式 曲线坐标系 逐维重构方法 |
| DOI：10.11887/j.cn.201602010 |
| 投稿日期：2015-09-19 |
| 基金项目:国防科学技术大学科研计划资助项目（ZDYYJCYJ20140101） |
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| High-order finite volume schemes in three-dimensional curvilinear coordinate system |
| XU Dan1, WANG Dongfang1, CHEN Yaming2, DENG Xiaogang1 |
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(1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;2. College of Science, National University of Defense Technology, Changsha 410073, China)
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| Abstract: |
| In order to develop a high-order finite volume scheme, which can perform with high fidelity in smooth regions, capture the discontinuities without oscillation, and overcome the difficulty in choosing stencils, a high-order finite volume scheme on structure meshes was developed on the basis of dimension-by-dimension reconstruction method. The scheme was also extended to the three-dimensional curvilinear coordinate system, which was suitable for the computation under relatively complex configurations. In order to validate the numerical scheme, some test cases were used. In the cases of the isentropic vortex and two-dimensional channel flow, it was found that the designed order of accuracy could be achieved. In the double Mach problem, it was proved that the scheme could well capture the discontinuities. The test cases show that the scheme has high numerical accuracy and robust capturing ability on curvilinear meshes and high efficiency in the simulations of the computational fluids dynamics. |
| Keywords: finite volume method high-order scheme curvilinear coordinate system dimension-by-dimension reconstruction method |
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