A new spectral method for direct numerical simulations of magnetohydrodynamic channel flows

Simulations of liquid metal flows in channel and duct configurations under a strong magnetic field pose a difficult problem for existing numerical methods. The main obstacle is the linear increase in number of modes required to resolve thin Hartmann boundary layers with the intensity of the magnetic field B. To overcome this problem we developed a new approach to the numerical calculations describing these flows. The solution of the flow is expressed in a base of eigenfunctions of the linear part of the governing equations and its adjoint, We show that in this approach the computational cost does not depend on the thickness of boundary layer and therefore it allows for performing calculations for high magnetic fields.