Fast Multigrid Solution of the Advection Problem
                         with Closed Characteristics

                                  I. Yavneh
           Technion---Israel Institute of Technology Haifa, Israel

                                 C.H. Venner
               University of Twente, Enschede, The Netherlands

                                  A. Brandt
                Weizmann Institute of Science, Rehovot, Israel

                                September 1995

The numerical solution of the advection-diffusion problem in the inviscid
limit with closed characteristics is studied as a prelude to an efficient high
Reynolds-number flow solver.  It is demonstrated by a heuristic analysis and
numerical calculations that using upstream discretization with downstream
relaxation-ordering in a multigrid cycle with appropriate residual weighting
leads to an efficient solution process.  Upstream finite-difference
approximations to the advection operator are derived whose truncation terms
approximate ``physical'' (Laplacian) viscosity, thus avoiding spurious
solutions to the homogeneous problem when the artificial diffusivity dominates
the physical viscosity.