初值方法求解柱几何线性磁流体内扭曲模和撕裂模问题

Using the Initial Value Method to Solve the Twisted and Teared Mode Problems in a Linear Magnetic Fluid with Cylindrical Geometry

基于非约化可压缩的磁流体模型开发了求解磁流体不稳定性问题的线性初值程序。使用初值程序研究了m/n=2/1撕裂模和m/n=1/1内扭曲模的增长率和模结构,并与本征值程序的结果进行了对比。结果表明:初值程序和本征值程序的结果吻合。分析了初值方法中增长率对时间步长和网格的依赖关系,给出了相应的时间步长取值估算式,解决了时间步长取值问题。当网格数较大时,初值程序在计算效率上展示出了极大的优势。此外,初值程序得到的解是唯一的,这可以省去复杂的本征值筛选流程。

Based on the non-reduced compressible magnetofluid model,a linear initial value program for solving the instability problem of magnetofluids is developed.The growth rate and the structure of the m/n=2/1 tearing mode and the m/n=1/1 internal distortion mode are studied by using the initial value program,and the results are compared with those obtained by the eigenvalue program.The results show that the results obtained by the initial value program and the eigenvalue program are in good agreement.The dependence of the growth rate on the time step and the number of meshes in the initial value method is analyzed,and the corresponding time step estimation formula is given to solve the problem of time step value.When the number of meshes is large,the initial value program shows great advantages in computing time.In addition,the solution obtained by the initial value program is unique,which can save the complex process of eigenvalue selection.