Analysis of robust multigrid methods for steady viscous low Mach number flows (Q1372022)

A theoretical and numerical analysis of different implicit methods in multigrid form is carried out in order to study their behaviour at various flow conditions. The Fourier analysis for scalar convection-diffusion equations is extended to the coupled set of laminar Navier-Stokes equations. For first- and second-order discretized Navier-Stokes equations, the analysis of point, line, and block methods is in good agreement with the numerical results. The influence on the convergence rate of different second-order implementations in the mutligrid method is also considered.