不可压磁流体力学方程组的高精度数值解法  

High Precision Numerical Method for the Incompressible Magnetohydrodynamics Equations

作　　者：庄昕 葛永斌 袁冬芳 ZHUANG Xin;GE Yongbin;YUAN Dongfang(School of Science,Henan University of Engineering,Zhengzhou 451191,China;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China;School of Science,Inner Mongolia University of Science and Technology,Baotou 014010,China)

机构地区：[1]河南工程学院理学院,河南郑州451191 [2]宁夏大学数学统计学院,宁夏银川750021 [3]内蒙古科技大学理学院,内蒙古包头014010

出　　处：《应用数学》2022年第1期180-189,共10页Mathematica Applicata

基　　金：国家自然科学基金(11901162);河南省高等学校重点科研项目计划基金(21A110006);河南工程学院博士基金项目(DKJ2019013)。

摘　　要：为数值求解低雷诺数下不可压流体在电磁场作用下的流动,提出一种四阶紧致差分方法.由二维原始变量的MHD方程组出发,推导出具有较少未知量的电流密度-涡量-流函数形式MHD方程组.建立了求解二维非定常不可压MHD方程组的电流密度-涡量-流函数形式的四阶精度紧致差分格式.为验证本文提出的高精度紧致差分方法的精确性和可靠性,对有解析解的二维非定常不可压MHD方程组的初边值问题进行数值模拟,数值结果证明本文所建立的高阶紧致格式精确有效并且无条件稳定.In this study, a four-order compact difference method for incompressible fluid flows in the presence of a magnetic field at low magnetic Reynolds number is proposed. Through the two-dimensional primitive variable MHD equations, we get the current density-vorticity-stream function MHD equations which have less variables. Then the fourth-order compact difference schemes is developed for solving two-dimensional time-dependent incompressible current density-vorticity-stream function MHD equations. In order to prove the accuracy and reliability of the high-order compact difference method, a numerical experiment with exact solutions to the two-dimensional time-dependent incompressible MHD equations with initial and boundary conditions is given. The numerical results demonstrate that the present high-order compact method is accurate, effective and unconditionally stable.

关 键 词：MHD方程组 紧致差分格式 高精度 涡量-流函数方法 

分 类 号：O241.82[理学—计算数学]