对流占优问题的一种修正CUI格式

A Modified CUI Scheme for Convection-Dominated Equations

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。

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.