The relaxation coefficients in Eq. 108 are defined
following P. Marbaix and van Ypersele (2003) as
Here, the coefficients approach their maximum values
over (5 or 9) points using one of the following
function options:
where
so that decreases from 1 (at the boundary) to 0 within the sponge
zone. is a parameter which controls the rate at which goes to
zero away from the lateral boundary. There really doesn't seem to be a
consensus in the literature on the best form for , which is why the
multiple options for are available for testing in ASP.
P. Marbaix and van Ypersele (2003) did a rather complete survey of relaxation methods, and
they recommended an exponential function for , however from tests
using ASP, the Gaussian (exponential) form (Eq. 113)
has been found to
give the best results and is thus the current default function. In
terms of the size of the sponge zone, the model currently uses as
P. Marbaix and van Ypersele (2003) showed that this configuration produces slight better
results than the 5-point form: indeed, tests with this model have
indicated the same conclusion, although generally the results using
the two values of are fairly similar with a slightly smoother
transition for the 9-point case.
ASP currently uses
(when )
or
(when ).