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比较多种数值方法在多种网格上解扩散对流问题之数值结果

阅读量:02021-10-11作者:张修铭来源:学术论文
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研究生: 张修铭
研究生(外文): Siou-Ming Jhang
论文名称: 比较多种数值方法在多种网格上解扩散对流问题之数值结果
论文名称(外文): A Comparison of Numerical Methods on Various Meshes for Convection-Diffusion Problems
指导教授: 施因泽
口试委员: 陈焜灿、简澄陞
口试日期: 2012-06-22
学位类别: 硕士
校院名称: 国立中兴大学
系所名称: 应用数学系所
学门: 数学及统计学门
学类: 数学学类
论文种类: 学术论文
论文出版年: 2012
毕业学年度: 100
语文别: 英文
论文页数: 49
中文关键词: 扩散对流问题、有限裁缝点法、调适网格
外文关键词: convection diffusion problem、tailored finite point method、layer-adaptive mesh


在这篇论文中,我们比较了中间差分法、Galerkin 有限单元法、流线迎风 Petrov-Galerkin 方法、裁缝有限点法解扩散对流问题的数值结果。我们将在均匀网格以及Shishkin 网格和 Bakhavalov-Shishkin网格这两种层流调适网格上实作这些数值方法。我们将在各种不同的网格上使用各种数值方法解三种层流问题。我们的结果显示有限裁缝点法不适合在层流调适网格上实作,而在均匀网格上,有限裁缝点法优于其他在不同的网格上实作的各种数值方法。


In this thesis, we compare various numerical methods: the central difference method (CDM), the Galerkin finite element method (GFEM), the Streamline-Upwinded Petrov-Galerkin method (SUPG) and a tailored finite point method (TFPM) for solving convection-diffusion problems. Our methods are implemented on the uniform mesh (U mesh) and the layer-adaptive meshes: the Shishkin mesh (S mesh) and the Bakhavalov-Shishkin mesh (BS mesh). In the experiments, we perform various numerical methods with different meshes on three types of layer problems. The results show that TFPM does not need to use the layer-adaptive mesh, and its best performance is on the U mesh in comparison with other discretizations on various meshes.


1 Introduction 1
1.1 History and motivation . . . 1
1.2 Notations . . . 2
2 Discretization of convection-diffusion equations 3
2.1 Central difference method . . . 3
2.2 Galerkin finite element method . . . 3
2.3 Streamline upwind/Petrov-Galerkin method . . . 4
2.4 Tailored finite point method . . . 5
3 Layer-adaptive meshes 8
3.1 Introduction . . . 8
3.2 Shishkin mesh . . . 9
3.3 Bakhvalov-Shishkin mesh . . . 11
3.4 The choice of the δR for the SUPG . . . 12
4 Experiments 13
4.1 Problem 1: Regular boundary layers . . . 14
4.2 Problem 2: Characteristic boundary layers . . . 27
4.3 Problem 3: Interior layers . . . 40
5 Conclusion 46


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扩散对流问题 有限裁缝点法 调适网格

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