二维定常对流扩散方程的一种高精度紧致差分方法
魏剑英
【期刊名称】《重庆理工大学学报（自然科学版）》 【年(卷),期】2012(026)002
【摘要】Based on the fourth-order Pade formula of the first and second-order derivatives, a fourth- order compact difference scheme is proposed for solving two-dimensional convection diffusion equa- tion. Fourth order explicit difference schemes are used to construct the same order discretization of boundary points. Then, the accuracy of the fourth-order compact difference schemes is upgraded to sixth-order by using Richardson extrapolation technique and operator interpolation scheme. Sixth-order explicit difference schemes of first and second-order derivatives on the boundaries are used. Finally, numerical experiments are given to prove the accuracy and efficiency of the present method.%对于二维对流扩散方程,利用一阶和二阶导数的四阶Padé型紧致差分逼近式,结合原方程,得到了求解该方程的一种四阶精度的隐式紧致差分格式。该格式在每个空间方向上只涉及到3个点处的未知量及导数值,对导数利用四阶显式偏心格式,然后利用Richardson外推法、算子插值法及导数在边界点处的六阶显式偏心格式,将构造的四阶紧致差分格式的精度提高到六阶。最后通过数值实验验证了该方法的精确性和有效性。 【总页数】6页(112-117)
【关键词】对流扩散方程;紧致格式;高精度;隐式差分;Richardson外推法;有限
二维定常对流扩散方程的一种高精度紧致差分方法
