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.)
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