西南石油大学学报(自然科学版) ›› 1985, Vol. 7 ›› Issue (1): 42-50.DOI: 10.3863/j.issn.1000-2634.1985.01.005

• 论文 • 上一篇    下一篇

对流扩散方程显式差分格式的稳定性

赵碧华   

  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:1985-02-20 发布日期:1985-02-20

THE STABILITY OF EXPLICIT DIFFERENCE SCHEMES OF THE CONVECTION-DIFFUSION EQUATION

Zhao Bihua   

  • Received:1900-01-01 Revised:1900-01-01 Online:1985-02-20 Published:1985-02-20

摘要: 到目前为止,人们在进行酸压施工设计,求解描述酸液浓度沿裂缝分布状况的对流扩散方程时,由于某些技术上原因均未考虑氢离子有效传质系数D_e随酸浓度C_D的变化规律。本文给出了在考虑D_e随C_D变化的条件下,用有限差分法求解对流扩散方程的过程。给出了对流扩散方程差分格式稳定性的求证方法以及该差分格式的稳定条件,并进一步给出了利用此稳定条件选取合理计算步长进行计算的结果。 在进行数理推证时,充分考虑了每一个物理量的特征,从而使推证简化。展示了数理方法求解工程问题的一个途经。

Abstract: Up to now, in acid treatment design at home and abroad, it has not been taken into account how the effective mass transfer coefficient of the hydrogen ion De varies with acid concentration Co in solving the convection-diffusion equation which shows the distribution of acid concentration along a fracture.In this paper, we have not only solved this equation by means of finite differences, considering the change of De with Co, but also shown the conditions of the stability and the method.