8.0
general documentation
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prehyd.f90 File Reference

Compute an "a priori" hydrostatic pressure and its gradient associated before the Navier Stokes equations (prediction and correction steps navstv.f90). More...

Functions/Subroutines

subroutine prehyd (grdphd, iterns)

Detailed Description

Compute an "a priori" hydrostatic pressure and its gradient associated before the Navier Stokes equations (prediction and correction steps navstv.f90).

This function computes a hydrostatic pressure $ P_{hydro} $ solving an a priori simplified momentum equation:

\[    \rho^n \dfrac{(\vect{u}^{hydro} - \vect{u}^n)}{\Delta t} =
    \rho^n \vect{g}^n - \grad P_{hydro}
\]

and using the mass equation as following:

\[    \rho^n \divs \left( \delta \vect{u}_{hydro} \right) = 0
\]

with: $ \delta \vect{u}_{hydro} = ( \vect{u}^{hydro} - \vect{u}^n) $

finally, we resolve the simplified momentum equation below:

\[    \divs \left( K \grad P_{hydro} \right) = \divs \left(\vect{g}\right)
\]

with the diffusion coefficient ( $ K $) defined as:

\[         K \equiv \dfrac{1}{\rho^n}
\]

with a Neumann boundary condition on the hydrostatic pressure:

\[       D_\fib \left( K, \, P_{hydro} \right) =
       \vect{g} \cdot \vect{n}_\ib
\]

(see the theory guide for more details on the boundary condition formulation).

Function/Subroutine Documentation

◆ prehyd()

subroutine prehyd ( double precision, dimension(ndim, ncelet) grdphd,
integer iterns )
Parameters
[out]grdphdthe a priori hydrostatic pressure gradient $ \partial _x (P_{hydro}) $
[in]iternsNavier-Stokes iteration number