188 1996 Lars Ferm, Per Lötstedt ferm@tdb.uu.se, Per.Lotstedt@saab.se Blockwise adaptive grids with multigrid acceleration for compressible flow Abstract In a multi-block code for compressible flow problems a method is introduced to adapt the cell resolution to control the numerical error in the steady state solution. The refinement and coarsening of the grid is based on an estimate of the discretization error. The convergence of the iterations is improved by the multigrid algorithm. The global grids at the multigrid levels are chosen to improve the efficiency. The Euler solution is computed with a three-grid algorithm around a three-dimensional wing. The accuracy and computational work are compared on a uniformly fine grid and the adapted grid.