Advanced Ocean Modelling: Using Open-Source Software

3.4 Nonhydrostatic Solver 31Fig. 3.6 Flow chart of the S.O.R. methodsimulation. This can be rather time consuming, particularly for three-dimensionalmodel applications.3.4.5 Boundary Conditions for Variable BathymetryVariable 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”. Horizontaland vertical velocity components are kept at zero values in dry grid cells during asimulation.Owing to the staggered nature of the Arakawa-C grid (see Fig. 3.3), additionalconditions 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 cellwith index (k + 1) is dry and by setting vertical velocity to zero if the overlying gridcell of index (i −1) is dry. Lateral flooding of coasts is not implemented here.3.4.6 Stability CriterionThe stability criterion for the finite-difference versions of Eqs. (3.15, 3.16, 3.17, and3.18) is given by:Δt ≤Δx √ghmax(3.35)