NND 格式在理想磁流体方程组中的应用  

APPLICATION OF NND SCHEME ON MAGNETO HYDRODYNAMICS EQUATIONS

作　　者：叶占银[1] 魏奉思[1] 李敬群[1] 冯学尚[1] 姚久胜[1] 

机构地区：[1]中国科学院空间科学与应用研究中心,北京100080

出　　处：《力学学报》2001年第3期301-308,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(49990453;49925412).

摘　　要：针对守恒型磁流体力学方程组（ＭＨＤ）和流体力学方程组（ＨＤ）通量项不同特点，提出 了一种能够采用无振荡、无自由参数（ＮＮＤ）格式离散ＭＨＤ方程组的通量分裂方法，并首先 在一维模型方程中验证了方法的可行性，进一步全三维离散了ＭＨＤ方程组，在轴对称盔形磁 场位形太阳风流动的数值试验中，选取４６个太阳半径（Ｒ_ｓ）的计算域，基本能够反映行星际 空间物理参数在径向有大到８～９个量级变化的特点．计算结果表明针对气动力学跨音速流动 的ＮＮＤ格式可以推广到磁流体力学方程组中，并有很好的稳定性．A flux vector splitting method, combined with Non-free parameter and Non-oscillation Difference scheme (NND) and constructed for magnetohydrodynamics (MHD ) equations with the consideration of difference between the flux vector of magnetohydrodynamics equations and that of Euler equations, is presented. First, it is tested to be effective on one-dimensional model equations, which include one for steady-state problem and one for time-variation problem. The numerical results agree very well with those of the exact solutions. Second, it is introduced in detail that how the flux vector splitting method combined with the NND scheme could be applied into the discretion of three-dimensional MHD equations and how the magnetic field is treated to reduce the effect of Lorentz force error caused by numerical non-zero magnetic divergence. In order to study the effectiveness of the algorithm, an example of solar wind flow in a helmet structure magnetic field is taken and the computation is carried out on a large domain (r: 1～ 46R_s) with a coarse mesh (mesh in radial direction: 46 points) to reflect the large variation of solar wind parameters in the interplanetary space. After iterating about 7000 steps on a PC586, the numerical variables begin to remain a steady state, the solution is smooth and spiral magnetic field, which agrees with interplanetary observation, appears.

关 键 词：太阳风 磁流体力学 MHD数值模拟 太阳磁场 数值算法 NND格式 理想磁流体方程组 

分 类 号：O361.3[理学—流体力学]