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

First and second order finite volume schemes for the solution of the steady Euler equations of 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, emphasizing the effect for the different possible discontinuities in the solution.