摘要
基于非均匀网格上函数的泰勒级数展开,结合残参量修正法,推导了非均匀网格上对流扩散方程的高阶指数型紧致差分格式,选取的算例表明,格式兼有高精度和高分辨率的优点,能够很好的适用于大梯度变化,计算区域中含边界层和对流占优区域中的流动问题的求解.
Based on Taylor＇s series expansion of continuous function on non-uniform grid and the residual correction method, a high order exponential compact finite difference scheme on non-uniform grid for 1D steady convection diffusion problems is developed, the numerical results of the selected case show that the present scheme has many advantages such as yielding more accurate numerical solutions, having high resolution for the boundary layers, being well suitable for both convection-dominant flow and diffusion-dominant flow, and so on.
出处
《数学的实践与认识》
北大核心
2015年第4期268-275,共8页
Mathematics in Practice and Theory
基金
宁夏自然科学基金(NZ12123)
关键词
对流扩散方程
非均匀网格
指数型差分格式
convection-diffusion equation
non-uniform grid
exponential finite difference scheme
