Multigrid acceleration of a flux-difference splitting method for steady Euler equations

AbstractA flux-difference splitting based on the polynomial character of the flux-vectors is introduced for steady Euler equations. This splitting is applied to finite volumes centered around the vertices of the computational grid. A discrete set of equations is obtained which is both conservative and positive. The flux-difference splitting is done in an algebraically exact way. As a consequence, shocks are represented as sharp discontinuities, without wiggles. Due to the positivity, the set of equations can be solved by collective relaxation methods.A full multigrid method based on symmetric successive relaxation, full weighting, bilinear interpolation and W-cycle is presented. Typical full multigrid efficiency is achieved for the GAMM transonic bump test case since after the starting cycle and one multigrid cycle, the solution cannot be distinguished anymore from the fully converged solution