Fast Multigrid Solution of the Advection Problem
with Closed Characteristics

Irad Yavneh
Department of Computer Science
Haifa 32000

C. H. Venner
University of Twente
The Netherlands

A. Brandt
Weizmann Institute of Science


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.

Contributed November 27, 1996.