Comparison of the simplified and full MHD models for laminar incompressible flow past a circular cylinder

Numerical simulations are carried out over a wide range of Hartmann number for steady-state laminar problems with both models. For the full model, magnetic Reynolds number (Rem) is chosen from 0.01 to 10. The computed results show that solutions of the simplified MHD model are not exactly the same as those of the full MHD model for this flow problem in most cases even if Rem in the full model is very low. Only in the special case that a strong external magnetic field is exerted perpendicular to the dominant flow direction, can the simplified MHD model be regarded as an approximation of the full MHD model with low Rem.