对流占优问题的一种修正CUI格式
A Modified CUI Scheme for Convection-Dominated Equations
DOI: 10.12677/AAM.2016.54083, PDF,    科研立项经费支持
作者: 吕娜, 高巍：内蒙古大学数学科学学院，内蒙古 呼和浩特；谢桃枫：内蒙古医科大学计算机信息学院，内蒙古 呼和浩特
关键词: CUI格式；Hermite插值；CBC/TVD；mCUI格式；CUI Scheme； Hermite Interpolation Polynomial； CBC/TVD； mCUI Scheme
摘要: 对流扩散方程是一类重要的模型方程，构造对流项的高分辨率离散格式是数值计算的关键，本文基于CBC (Convection Boundedness Criterion)准则和TVD (Total Variational Diminishing Constraint)准则，利用Hermite插值，构造一种改进的CUI格式。经典的算例表明，此数值方法不仅能很好的抑制线性对流离散格式的数值振荡，也表现出良好的数值计算精度。
Abstract: In this paper, a modified CUI scheme is presented for discretizing the convection term. Coupled with Herimite interpolation, CBC (Convection Boundedness Criterion) and TVD (Total Variational Diminishing Constraint) are applied to suppress numerical oscillations. Typical test cases demonstrate that the present scheme possesses the boundedness of convection and high accuracy.
文章引用：吕娜, 谢桃枫, 高巍. 对流占优问题的一种修正CUI格式[J]. 应用数学进展, 2016, 5(4): 716-727. https://dx.doi.org/10.12677/AAM.2016.54083

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