Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers

Steady incompressible flow around a circular cylinder in anexternal magnetic field that is aligned with fluid flow directionis studied for Re (Reynolds number) up to 40 and theinteraction parameter in the range 0≤N≤15 (or 0≤M≤30), where M is the Hartmann number related to N by therelation M=2NRe, using finite difference method.The pressure-Poisson equation is solved to find pressure fields inthe flow region. The multigrid method with defect correctiontechnique is used to achieve the second-order accurate solution ofcomplete nonlinear Navier-Stokes equations. It is found that theboundary layer separation at rear stagnation point for Re=10is suppressed completely when N<1 and it started growing againwhen N≥9. For Re=20 and 40, the suppression is notcomplete and in addition to that the rear separation bubblestarted increasing when N≥3. The drag coefficient decreasesfor low values of N(<0.1) and then increases with increaseof N. The pressure drag coefficient, total drag coefficient, andpressure at rear stagnation point vary with N. It is also found that the upstream and downstream pressures on the surface ofthe cylinder increase for low values of N(<0.1) and rear pressure inversion occurs with further increase of N. These results are in agreement with experimental findings