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Implicit Free Surface: Velocity Formulation

Equation ([*]) can be solved explicitly for the depth field at the arrival point in terms of the divergence of the velocity field as

where

Further, ([*]) can be simplified to express in terms of as follows,

where

If we then insert ([*]) into ([*]) and assume as known, then we have a linear elliptic equation for ,

where the right-hand-side is known and is the linear elliptic operator such that

Equations ([*]) and ([*]) constitute our implicit free surface semi-Lagrangian shallow water model formulated in terms of an elliptic equation for the velocity field.



Balasubramany (Balu) Nadiga
1/8/1998