对流占优扩散问题的高精度守恒分裂方法研究  

High Accurate Conservative Splitting Methods for Convection-Dominated Diffusion Problems

作　　者：郑岩杰 付凯 Zheng Yanjie;Fu Kai(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2022年第S01期107-115,共9页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11601497);山东省自然科学基金项目(ZR2021MA005)资助。

摘　　要：本文研究了高维对流扩散方程的高阶守恒维数分裂方法。该方法具有空间四阶精度和时间二阶精度,且可应用大时间步长进行计算,提高计算效率。通过理论分析证明了格式的守恒性质,并进一步通过数值算例验证了方法的精度和守恒性。In this paper, the high-order conservative dimensional splitting methods for convection diffusion equations are studied. The proposed schemes have spatial fourth-order accuracy and temporal second-order accuracy. Large time steps are permitted in the computation, which improve the computational efficiency. The mass conservation properties of the schemes are proved by the radical andysis. Numerical examples demonstrate the accuracy and mass conservation of the methods.

关 键 词：对流扩散方程 对流占优 质量守恒 Semi-Lagrangian方法 维数分裂方法 

分 类 号：O242[理学—计算数学]