FAST MULTIGRID SOLUTION OF THE ADVECTION PROBLEM WITH CLOSED CHARACTERISTICS

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

(Joint work with:

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

Achi Brandt, The Weizmann Institute of Science, Rehovot, Israel.)

                      ABSTRACT

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 
and appropriate residual weighting in a simple multigrid V cycle 
produces an efficient solution process.
We also derive upstream finite-difference approximations to the 
advection operator, whose truncation terms approximate "physical" 
(Laplacian) viscosity, thus avoiding spurious solutions to the 
homogeneous problem when the artificial diffusivity dominates the 
physical viscosity.