三维理想MHD方程数值求解方法研究  

Numerical study on ideal three-dimensional MHD equations

作　　者：潘勇[1] 王江峰[1] 伍贻兆[1] 

机构地区：[1]南京航空航天大学航空宇航学院,江苏南京210016

出　　处：《中国科学技术大学学报》2008年第5期534-541,共8页JUSTC

基　　金：国家自然科学基金(10402013)资助

摘　　要：针对三维理想MHD方程提出了一种新的雅可比矩阵分裂方法,并成功地应用于磁场干扰下的三维高超声速磁流场流数值模拟.控制方程在非结构网格上采用有限体积法进行空间离散,其中对流项采用新的逆风向量分裂格式,并引入了双曲型磁场散度清除技术,时间推进为显式5步龙格-库塔方法.首先,对三维MHD管道压缩流动进行了数值模拟,得到了与参考文献相吻合的数值结果.然后,分别对三维有、无均匀磁场干扰下的高超声速半球体绕流流场进行了数值模拟,对比发现两者的流场结构存在明显的差异,有磁场干扰时壁面上的压力和温度要低于无磁场干扰时的情况,得到的数值结果与理论分析相符合.A new Jacobian matrix splitting method for ideal three-dimensional MHD （magnetohydrodynamics） equations was developed and verified by numerically simulating 3D hypersonic MHD flows. The numerical scheme is established on unstructured meshes using the finite volume method, the inviscid fluxes are approximated using flux-vector splitting method with the ncw Jacobian matrix splitting and the time integration is a 5-stage explicit Runge-Kutta scheme. A hyperbolic divergence cleaning technique is introduced to avoid the magnetic divergence errors. The accuracy of the algorithm is explored by solving 3D supersonic channel flows around compression corners, where the same results as those in the references are obtained. Then, this numerical method is applied to simulate 3D hypersonic plasma flow around hemisphere with the effect of magnetic field, numerical results are obtained and compared with those without magnetic field effect. Results show the great differences in flow structure between the two kinds of flows, flow with magnetic field gets lower pressure and temperature on the wall, which matches well to the theoretical analysis.

关 键 词：非结构网格 三维理想MHD方程 逆风通量分裂 散度清除 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]