Numerical simulations of highly non-linear coupled full MHD equations in spherical geometry

Abstract

Numerical simulations have been performed to solve highly non-linear coupled full MHD equations in spherical polar coordinates. The control of flow separation behind a sphere using Lorentz forces is investigated at moderate magnetic Reynolds numbers. An external magnetic field is applied in the direction of the steady, viscous and electrically conducting flow such that it is aligned at large distances from the sphere. The governing equations are coupled non-linear Navier–Stokes and non-linear Maxwell's equations. The parameters that governs the flow are Reynolds number Re, magnetic Reynolds number Rm and Alfvén number β. The finite difference method combined with multigrid technique is used to solve the full MHD equations which are expressed in vorticity, stream function and magnetic stream function form. All the non-linearities in the momentum equation due to Lorentz force are handled effectively. It is found that the separation for highly conducting fluids can be suppressed with low magnetic fields. The drag coefficient is found to decrease for β≤1 and then increase. The results agree with experimental results.