Solution-adaptive multigrid for steady gas dynamics problems

This paper consists of two parts. In the first part we give a review of a good multigrid method for solving the steady Euler equations of gas dynamics on a locally refined mesh. The method is self-adaptive and makes use of unstructured grids that can be considered as parts of a nested sequence of structured grids. It is briefly described and applied to some steady Euler-flow problems. The method appears to be much more accurate and efficient than the corresponding multigrid method that applies global refinements only. In the second part of the paper, vectorisation of the code is treated. To enable this vectorisation, index arrays are introduced and added to the quad-tree type data-structure that is applied in the scalar case. Speed-up factors are given for the same test cases as considered in the first part of the paper. The results are most satisfactory