Agglomeration Multigrid for the Three-dimensional Euler Equations

A multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the threedimensional Euler equations on unstructured grids about complex con gurations. It is shown that the agglomeration procedure can be tailored to achieve certain coarse grid properties such as the sizes of the coarse grids and aspect ratios of the coarse grid cells. The agglomeration is done as a preprocessing step and runs in linear time. The implications for multigrid of using arbitrary polyhedral coarse grids are discussed. The agglomeration multigrid technique compares very favorably with existing multigrid procedures both in terms of convergence rates and elapsed times. The main advantage of the present approach is the ease with which coarse grids of any desired degree of coarseness may be generated in three dimensions, without being constrained by considerations of geometry. Inviscid ows over a variety of complex con gurations are computed using the agglomeration multigrid strategy. Part of this work was done while the author was employed by Computer Sciences Corporation, Mo ett Field, CA during which time the work was supported by the National Aeronautics and Space Administration under the NASA contract NAS 2-12961. This research was also supported under the NASA contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681. This research was supported by the National Aeronautics and Space Administration under the NASA contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681.