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

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 ββ. 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≤1β≤1 and then increase. The results agree with experimental results.

► Non-linear N-S equations coupled with non-linear Maxwell's equations are simulated in spherical geometry for the first time.
► The body force term (Lorentz force) introduces many non-linearities which are handled very effectively.
► The finite difference scheme combined with multigrid method is used to solve the governing equations.
► The defect correction technique is used to achieve second order accuracy.
► The results agree with the experimental results of Kim and Lee, Josserand et al., and Maxworthy.