Recall that the evaluation of the pressure requires the *
normalized* modes. The normalization constant is

The integral term can be evaluated by the trapezoidal rule. That is,

where

In problems with density discontinuities, the trapezoidal rule is
applied separately within each smooth region. Finally, the
derivatives can be either evaluated analytically
or by a simple centered-difference formula depending on their
complexity. In order to accommodate a wide variety of boundary conditions
without over-complicating the code,
* KRAKEN*
uses the difference approach.

Tue Oct 28 13:27:38 PST 1997