一种新的用于MHD方程逆风格式的Jacobian矩阵分裂方法

针对理想MHD方程,提出了一种新的基于MacCormack算法的雅可比矩阵分裂方法,克服了原有方法稳定性差的问题,并成功地应用于理想MHD方程的求解.控制方程在非结构混合网格上进行空间离散,其中对流项采用本文发展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.对MHD激波管流动和带均匀磁场干扰的二维高超声速钝头体绕流流场进行了数值模拟,得到了与参考文献相吻合的数值结果,表明本文发展的数值分裂方法可以有效地捕捉MHD流场的流动特征,并且具有比MacCormack方法更高的稳定性和计算精度.

A new Jacobian matrix splitting method for idea MHD equations

Based on MacCormack's scheme and considering its weak instability,a new Jacobian matrix splitting method for the idea MHD equations is developed and verified by test cases.The numerical scheme is established on hybrid meshes using finite volume method,the inviscid fluxes are approximated using the flux-vector splitting method with the new 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.This numerical scheme is implemented successfully in two typical problems,named MHD shock tube problem and 2D hypersonic plasma flow with magnetic field.Numerical results,which match well to those of limited references,demonstrate higher capabilities in shock capturing of the scheme to the MHD flowfield,and better stability than MacCormack's method.