Ab. Fortunato et Am. Baptista, VERTICAL DISCRETIZATION IN TIDAL FLOW SIMULATIONS, International journal for numerical methods in fluids, 22(9), 1996, pp. 815-834
We propose an empirical law for vertical nodal placement in tidal simu
lations that depends on a single parameter p. The influence of dimensi
onless numbers on the optimal value of p is analysed through a series
of numerical experiments for an individual vertical and a single value
of p is found to be adequate for all cases. The proposed law can lead
to gains in accuracy of over two orders of magnitude relative to a un
iform grid and compares favourably with non-uniform grids previously u
sed in the literature. In practical applications the most effective us
e of this law may require each vertical to have a different number of
nodes. Criteria for the distribution of the total number of nodes amon
g different verticals are also proposed, based on the concept of equal
izing errors across the domain. The usefulness of the overall approach
is demonstrated through a two-dimensional laterally averaged applicat
ion to a synthetic estuary.