Optimal Linear Growth of MHD Flow in a Square Duct

Transient linear growth of perturbations in fully developed liquid metal flow subjected to a vertical magnetic field (magnetohydrodynamic flow) is investigated. The flow is confined in an electrically insulating duct with square cross-section. A high order finite difference method called FD-q method is used to discretize the two-dimensional differential linear stability equations. The proposed FD-q method is found to have significant advantage on solving optimal linear energy amplification for duct flows. The optimal transient amplifications for different Fourier modes or different Hartmann numbers are in excellent agreement with the work of Biau et al and Krasnov et al. And the FD-q method may be further used for detail investigations on laminar-turbulent transition process in magnetohydrodynamic duct flows.