A Velocity-pressure Coupling Based Consistent and Conservative Method for MHD Flow

The finite volume method with collocated grid is applied to investigate MHD flows with low magnetic Reynolds number and high Ha number. A consistent and conservative scheme with higher accuracy is employed to calculate the current density and the Lorentz force. A modified momentum interpolation (MMI) velocity-pressure coupled algorithm is developed for the solution of incompressible Navier-Stokes equations with the Lorentz force included. The implicit pressure-velocity coupling is implemented by treating the pressure gradient term implicitly with Gauss theorem in discretizing momentum equation and using MMI to derive continuity equations. Compared with original momentum interpolation (OMI), MMI method possesses advantages of converged results time-step independence for transient flow problems. Furthermore, a grid skew correction term is applied into MMI to reduce numerical error. Both the time and space are discretized in a second order accuracy. At last, the 3D simulation code is tested by CFD benchmark cases and the results shows good consistency.