  Coarse grid projection (CGP) is a multiresolution technique for accelerating
numerical calculations associated with a set of nonlinear evolutionary
equations along with the stiff Poisson equations. In this article we use CGP
for the first time to speed up incompressible magnetohydrodynamics (MHD) flow
simulations. Accordingly, we solve the nonlinear advection-diffusion equation
on a fine mesh, while we execute the electric potential Poisson equation on the
corresponding coarsened mesh. Mapping operators connect two grids together. A
pressure correction scheme is used to enforce the incompressibility constrain.
The study of incompressible flow past a circular cylinder in the presence of
Lorentz force is selected as a benchmark problem with a fixed Reynolds number
but various Stuart numbers. We consider two different situations. First, we
only apply CGP to the electric potential Poisson equation. Second, we apply CGP
to the pressure Poisson equation as well. The maximum speedup factors achieved
here are approximately 3 and 23 respectively for the first and second
situations. For the both situations we examine the accuracy of velocity and
vorticity fields as well as the lift and drag coefficients. In general, the
results obtained by CGP are in an excellent to reasonable range of accuracy and
are significantly consistently more accurate than when we use coarse grids for
the discretization of both the advection-diffusion and electric potential
Poisson equations.
