MULTIGRID SOLUTION OF STEADY EULER EQUATIONS BASED ON POLYNOMIAL FLUX-DIFFERENCE SPLITTING

A-flux-difference splitting based on the polynomial character of the flux vectors is applied to steady Euler equations, discretized with a vertex-centred finite volume method. In first order accurate form, a discrete set of equations is obtained which is both conservative and positive. Due to the positivity, the set of equations can be solved by collective relaxation methods in multigrid form. A full multigrid method based on successive relaxation, full weighting, bilinear interpolation and W-cycle is used. Second order accuracy is obtained by the Chakravarthy-Osher flux-extrapolation technique, using the Roe-Chakravarthy minmod limiter. In second order form, direct relaxation of the discrete equations is no longer possible due to the loss of positivity. A defect-correction is used in order to solve the second order system.