A multigrid algorithm for the incompressible Navier-Stokes equations

Publisher Summary This chapter presents a fast multigrid solver for the steady incompressible Navier–Stokes equations. With this approach, the spatial discretization correctly distinguishes between the advection and elliptic parts of the operator, allowing an efficient smoother to be constructed. Numerical results are shown for flow over a Karman–Trefftz airfoil at angle of attack. Using Gauss–Seidel line relaxation in both the radial and azimuthal directions, multigrid convergence behavior approaching that of O ( N ) methods is achieved. Rapid multigrid convergence is achieved for advection-dominated flows by designing a solver that effectively distinguishes between the elliptic, parabolic, and hyperbolic factors of the system and treats each one appropriately. For instance, advection can be treated by space marching, while elliptic factors can be treated by multigrid.