| A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD |
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| 引用本文： | 魏剑英,葛永斌. A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD[J]. 应用数学和力学, 2022, 43(2): 187-197. DOI: 10.21656/1000-0887.420151 |
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| 作者姓名： | 魏剑英 葛永斌 |
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| 作者单位： | 宁夏大学 数学统计学院，银川 750021 |
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| 基金项目： | 国家自然科学基金(12161067,11961054,11902170);宁夏自然科学基金(2020AAC03059);宁夏自治区青年拔尖人才培养工程项目。 |
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| 摘 要： | 针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式，对空间的离散采用四阶紧致差分方法，对时间的离散采用Taylor级数展开和余项修正技术，所提格式在时间上的精度为二阶、在空间上的精度为四阶。利用Fourier稳定性分析法证明了该格式是无条件稳定的。最后给出数值算例验证了理论结果。
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| 关 键 词： | 对流扩散反应方程 变对流项和反应项系数 高精度紧致格式 无条件稳定 有限差分法 |
| 收稿时间： | 2021-06-03 |
A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations |
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| WEI Jianying,GE Yongbin. A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 187-197. DOI: 10.21656/1000-0887.420151 |
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| Authors: | WEI Jianying GE Yongbin |
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| Affiliation: | School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China |
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| Abstract: | Based on the 4th-order compact difference scheme for spatial discretization,the Taylor series expansion and the error remainder correction method for temporal discretization,a high-order compact finite difference scheme for solving the 3D unsteady convection diffusion reaction equations was proposed.The unconditional stability was proved with the Fourier analysis method.The proposed scheme has 2nd-order accuracy in time and 4th-order accuracy in space.At last,numerical examples validate the theoretical results. |
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| Keywords: | convection diffusion reaction equation variable convection and reaction coefficient high-order compact scheme unconditionally stable finite difference method |
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