Gas-Kinetic BGK Scheme for Three Dimensional Magnetohydrodynamics  

作　　者：Huazhong 

机构地区：[1]CAPT & LMAM of School of Mathematical Sciences, Peking University, Beijing 100871, China [2]Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong [3]Department of Mechanical & Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003-8001, USA

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2010年第4期387-404,共18页高等学校计算数学学报（英文版）

基　　金：supported by the National Basic Research Program under the Grant 2005CB321703;the National Natural Science Foundation of China(No.10925101 and No.10828101);the Doctoral Program of the Education Ministry of China(No.20070001036);the Program for New Century Excellent Talents in University(No.NCET-07-0022);supported by Hong Kong Research Grant Council 621709;National Natural Science Foundation of China(Project No.10928205);National Key Basic Research Program(2009CB724101)

摘　　要：The gas-kinetic theory based flux splitting method has been successfully proposed for solving one-and two-dimensional ideal magnetohydrodynamics by Xu et al. [J.Comput.Phys.,1999;2000],respectively.This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations,where an adaptive parameter 17 is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.The gas-kinetic theory based flux splitting method has been successfully proposed for solving one- and two-dimensional ideal magnetohydrodynamics by Xu et al.[J. Comput. Phys., 1999; 2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter η is used to control the numerical dissipation in the flux splitting method.Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.

关 键 词：The kinetic BGK scheme     magnetohydrodynamics     divergence-free condition 

分 类 号：O1[理学—数学]