Development of multigrid algorithms for problems from fluid dynamics

A Carterian multigrid algorithm for inviscid compressible two dimensional subsonic potential flow around a profile was developed. It features lexicographic column relaxation, standard full weighting of residuals, and bilinear interpolation of corrections. Circulation to fulfill the discrete Kutta-Joukowsky condition is changed only on the coarsest grid. Residual reduction factors per cycle of 0.05 to 0.1 are obtained. Results using the adaptive grid refinement technique are shown. The mesh size of the finest grid is hx = hy = 1/183. The iteration on this grid was terminated after the maximum residual was below the bound of 0.000005. Computing time is 15 to 19 sec on an IBM 3083 B Computer (BS-3000 FORTRAN 77, OPT=3). The total number of grid points used is 15,000.