FAST MULTIGRID SOLUTION OF THE ADVECTION PROBLEM WITH CLOSED CHARACTERISTICS

The numerical solution of the advection-diffusion problem in the invis cid limit with closed characteristics is studied as a prelude to an ef ficient high Reynolds-number ow solver. It is demonstrated by a heuris tic analysis and numerical calculations that using upstream discretiza tion with downstream relaxation ordering in a multigrid cycle with app ropriate residual weighting leads to an efficient solution process. Up stream finite-difference approximations to the advection operator are derived whose truncation terms approximate ''physical'' (Laplacian) vi scosity, thus avoiding spurious solutions to the homogeneous problem w hen the artificial diffusivity dominates the physical viscosity [A. Br andt and I. Yavneh, J. Comput. Phys., 93 (1991), pp. 128-143].