3.4 Nonhydrostatic Solver
31
Fig. 3.6 Flow chart of the S.O.R. method
simulation. This can be rather time consuming, particularly for three-dimensional
model applications.
3.4.5 Boundary Conditions for Variable Bathymetry
Variable bathymetry requires flow normal to a solid boundary to vanish. To this end,
a logical array is used as to indicate whether a grid cell is “dry” or “wet”. Horizontal
and vertical velocity components are kept at zero values in dry grid cells during a
simulation.
Owing to the staggered nature of the Arakawa-C grid (see Fig. 3.3), additional
conditions are required to make sure the absence of flow across solid boundaries.
This is achieved by setting horizontal velocity to zero value if the adjacent grid cell
with index (k + 1) is dry and by setting vertical velocity to zero if the overlying grid
cell of index (i −1) is dry. Lateral flooding of coasts is not implemented here.
3.4.6 Stability Criterion
The stability criterion for the finite-difference versions of Eqs. (3.15, 3.16, 3.17, and
3.18) is given by:
Δt ≤
Δx
√
gh max
(3.35)
31
Fig. 3.6 Flow chart of the S.O.R. method
simulation. This can be rather time consuming, particularly for three-dimensional
model applications.
3.4.5 Boundary Conditions for Variable Bathymetry
Variable bathymetry requires flow normal to a solid boundary to vanish. To this end,
a logical array is used as to indicate whether a grid cell is “dry” or “wet”. Horizontal
and vertical velocity components are kept at zero values in dry grid cells during a
simulation.
Owing to the staggered nature of the Arakawa-C grid (see Fig. 3.3), additional
conditions are required to make sure the absence of flow across solid boundaries.
This is achieved by setting horizontal velocity to zero value if the adjacent grid cell
with index (k + 1) is dry and by setting vertical velocity to zero if the overlying grid
cell of index (i −1) is dry. Lateral flooding of coasts is not implemented here.
3.4.6 Stability Criterion
The stability criterion for the finite-difference versions of Eqs. (3.15, 3.16, 3.17, and
3.18) is given by:
Δt ≤
Δx
√
gh max
(3.35)