A modified full multigrid algorithm for the Navier–Stokes equations

A modified full multigrid (FMG) method for the solution of the Navier–Stokes equations is presented. The method proposed is based on a V-cycle omitting the restriction procedure for dependent variables but retaining it for the residuals. This modification avoids possible mismatches between the mass fluxes and the restricted velocities as well as the turbulent viscosity and the turbulence quantities on the coarse grid. In addition, the pressure on the coarse grid can be constructed in the same way as the velocities. These features simplify the multigrid strategy and corresponding programming efforts. This algorithm is applied to accelerate the convergence of the solution of the Navier–Stokes equations for both laminar and high-Reynolds number turbulent flows. Numerical simulations of academic and practical engineering problems show that the modified algorithm is much more efficient than the FMG–FAS (Full Approximation Storage) method.