| 二维非定常对流扩散方程的对角占优隐格式及多重网格算法 |
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| 引用本文： | 黄文艳,葛永斌,杨绍华.二维非定常对流扩散方程的对角占优隐格式及多重网格算法[J].宁夏大学学报(自然科学版),2009,30(1):1-5. |
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| 作者姓名： | 黄文艳 葛永斌 杨绍华 |
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| 作者单位： | 宁夏大学,数学计算机学院,宁夏,银川,750021 |
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| 基金项目： | 国家自然科学基金，宁夏高等学校科学技术研究基金 |
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| 摘 要： | 提出了一种数值求解二维非定常变系数对流扩散方程的对角占优、空间为二阶精度的隐格式。利用Fourier分析方法证明了该格式是无条件稳定的．由于格式具有对角占优性，因此适用于大梯度（高雷诺数）问题的数值求解．另一方面，为了克服传统迭代法在求解隐格式时收敛速度慢的缺陷，采用了多重网格加速技术，大大加快了迭代收敛速度，提高了求解效率．数值实验结果证明了该格式的精确性、稳定性和对高网格雷诺数问题的强适应性．
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| 关 键 词： | 对流扩散方程 隐格式 对角占优 有限差分法 多重网格法 |
Diagonally Dominant Implicit Scheme and Multigrid Algorithm for 2-D Unsteady Convection Diffusion Equation |
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| Huang Wenyan,Ge Yongbin,Yang Shaohua.Diagonally Dominant Implicit Scheme and Multigrid Algorithm for 2-D Unsteady Convection Diffusion Equation[J].Journal of Ningxia University(Natural Science Edition),2009,30(1):1-5. |
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| Authors: | Huang Wenyan Ge Yongbin Yang Shaohua |
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| Institution: | School of Mathematics and Computer Science;Ningxia University;Yinchuan 750021;China |
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| Abstract: | A diagonally dominant second-order accurate implicit scheme is proposed to solve the two-dimensional unsteady convection diffusion equations with variable coefficients,and unconditional stability of it is proved by Fourier analysis.Large gradient problems(high Reynolds number problems) are suited due to diagonally dominant of the scheme.On the other hand,a multigrid method is presented to overcome the difficulties when traditional relaxation methods are used to treat the implicit difference schemes and a fa... |
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| Keywords: | convection diffusion equation implicit scheme diagonally dominant finite difference method multigrid method |
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