NND格式在多维理想磁流体方程组中的应用

采用修正的四步Runge-Kutta方法求解三维一般曲线坐标系下的理想磁流体方程组,为克服数值振荡,加特征型NND格式进行后处理.特征型NND格式推广到求解三维磁流体(MHD)问题需要知道雅可比通量的左右特征矩阵,在具体计算时需要克服矩阵的奇性.本文用三维程序采用推广的特征NND格式计算了一维MHD激波管和二维(MHD)喷管流动,计算结果表明,特征NND格式保持了TVD格式高精度的优点,又具有计算简单的特点,在包括强弱间断等复杂波系的定常和非定常MHD流场数值模拟中是成功的.

NND scheme's application in multi-dimensional ideal magnetohydrodynamic equations

A four-stage modified Runge-kutta scheme was applied to solve the ideal three-dimensional magnetohydrodynamic(MHD) equations in generalized curvilinear coordinate system, and a characteristic type NND scheme was added in post-processing to overcome numerical oscillation. The left and right eigen matrices should be needed when using this NND scheme to solve the three-dimensional MHD flow and the singular problem should be overcome. In this paper, the one dimensional MHD shock tube problem and two dimensional MHD nozzle flow are calculated using the three-dimensional code with this NND scheme. This NND scheme has been shown to possess both the high accuracy property of the TVD type schemes and the pithiness in formulation and code programming. The method has the ability to capture the complex waves with strong or weak discontinuities in steady or unsteady MHD flow simulation.