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### Bottom Boundary Conditions II:

Alternatively, the values of the variables themselves could be set for the inflows.

Outflow boundaries:

• Use one-sided derivatives to calculate

• Set , for fixed given values of the bottom density and energy.
• Calculate the values of the variables from the boundary equations (53-56).

Inflow boundaries:

• Impose a given entropy by adjusting and consitent with no reflected waves,

which reduces to hydrostatic equilibrium when the velocity, .

where

Then

where

Since

then

In general, solve for .

Drop the mass and energy conservation equations from the boundary conditions. The density and energy are set by this condition.

• Make the net mass flux tend toward zero with time constant . If (the time step) then the mass flux is kept instantaneously zero. Let

Set inflow vertical momentum (mass flux) to

Drop the vertical momentum conservation equations from the boundary conditions because is set by this condition.

Viggo Hansteen
Wed Sep 19 18:16:24 MET DST 2001