磁流体方腔槽道流整体线性稳定性数值方法研究

将Chebyshev谱配置法和基于非均匀网格的高阶FD-q差分格式运用于磁流体方腔槽道流整体线性稳定性研究，比较两类数值方法的优缺点.Chebyshev谱配置法收敛快且精度高，但需要构造非常庞大的满矩阵，存储量和计算开销巨大；高阶FD-q差分格式采用了基于Kosloff-Tal-Ezer变换的Chebyshev谱配置点作为离散网格，在保持较高网格收敛精度的同时，差分格式可以采用稀疏矩阵进行存储，显著降低了存储量和计算开销.相比传统的谱配置法，基于非均匀网格的高阶FD-q差分格式计算效率得到显著的提升，将高阶FD-q差分格式运用于非正则模线性最优瞬态增长的计算，计算效果良好.

Numerical Methods for Linear Global Stability of Magnetohydrodynamic Duct Flows

Spectral Chebyshev collocation method and high-order FD-q finite difference method are used for global instability analysis of magetohydrodynamic(MHD) duct flows and compared for their merits and drawbacks. Spectral Chebyshev collocation method has faster convergence rate and high-order accuracy, while it needs to construct full general eigenvalue matrix which would consume large memory storage and a great deal of computational cost. High-order FD-q finite difference method adopts modified Chebyshev collocation points as discretization mesh grids based on Kosloff-Tal-Ezer transformation. FD-q method can maintain high convergence rate of mesh grids, and resulted general eigenvalue matrix is very sparse and can be stored with sparse matrix, which greatly reduces computational resource. In contrast to traditional spectral collocation method, non-uniform mesh based FD-q method obtains remarkable progress on computational efficiency, which is further demonstrated by computation of linear optimal transient growth for MHD duct flows.