Defect correction and higher order schemes for the multigrid solution of the steady Euler equations

In this paper first- and second-order finite volume schemes for the solution of the steady Euler equations for inviscid flow are described. The solution for the first-order scheme can be efficiently computed by a FAS multigrid procedure. Second-order accurate approximations are obtained by linear interpolation in the flux- or the state space. The corresponding discrete system is solved (up to truncation error) by defect correction iteration. An initial estimate for the second-order solution is computed by Richardson extrapolation. Examples of computed approximations are given, with emphasis on the effect for the different possible discontinuities in the solution.