TY - JOUR
T1 - Fast multigrid solution of the advection problem with closed characteristics
AU - Yavneh, Irad
AU - Venner, Cornelis H.
AU - Brandt, Achi
PY - 1998
Y1 - 1998
N2 - 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 [A. Brandt and I. Yavneh, J. Comput. Phys., 93 (1991), pp. 128--143].
AB - 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 [A. Brandt and I. Yavneh, J. Comput. Phys., 93 (1991), pp. 128--143].
U2 - 10.1137/S1064827596302989
DO - 10.1137/S1064827596302989
M3 - Article
SN - 1064-8275
VL - 19
SP - 111
EP - 125
JO - SIAM journal on scientific computing
JF - SIAM journal on scientific computing
IS - 1
ER -