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.