Defect Correction and Nonlinear Multigrid for Steady Euler Equations

In this chapter we give a description of a multigrid method developed for the steady Euler and Navier-Stokes equations. The discretization method is based on cell-centered finite volumes. The solution method, that does not use time stepping, is based on nonlinear multigrid iteration (FAS). The method gets many of its good properties by the use of a sequence of first-order discretizations, based on a variant of Osher's approximate Riemann solver. Higher-order accuracy is obtained by defect correction iteration.