Defect correction and nonlinear multigrid for the steady Euler equations

In this chapter we describe an accurate, efficient and robust technique to solve the steady Euler equations for inviscid flow by a nonlinear multigrid method. The discretization is a finite volume one, using the Godunov scheme, with Osher's approximate Riemann solver as the numerical flux function. Nonlinear FAS multigrid cycling is used to directly solve the first-order discrete equations. Defect correction is used to obtain higher-order accuracy. The technique can be extended to the N avier-Stokes equations, and can be combined with the adaptive grid refinements.