基于Leonard规正变量的修正高分辨率组合格式

The Modified High-resolution Composite Scheme Based on the Leonard Normalized Variable

通过对规正变量进行重构,本文提出了求解对流扩散方程的修正高分辨率组合格式,它能够求解边界层和大梯度等问题.首先,根据规正变量的定义得出了组合格式的通用表达式,然后对时间项采用二阶中心差分格式,得到了对流扩散方程的离散表达式,对离散化得到的代数方程组采用TDMA算法求解,并推导出了组合格式计算过程迭代收敛时所满足的充分条件.数值实验表明:新格式具有分辨率高,数值耗散较低,总偏差量较小,能很好模拟场变量的大梯度变化,计算结果优于传统格式.

Based on the normalized variable, a modified high-resolution composite scheme is proposed to solve the convection-diffusion equation, which can be used to describe boundary layer problems or locally large gradient problems. Firstly, the generic form for the composite scheme is derived according to the definition of the normalized variable. Then, the second order central difference scheme is used to discretize the temporal derivative term. The discrete algebraic equations are solved with the TDMA algorithm. Thus, the sufficient condition for the convergence of the composite scheme is obtained. The numerical tests are presented to verify the effectiveness of the scheme. The numerical results show that the new format has higher resolution, lower numerical dissipation and smaller total amount of deviation when compared with traditional formats. The new scheme is good at simulating the large gradient field variables.