|  | programmer's documentation | 
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 (prhyd, grdphd) | 
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  solving an a priori simplified momentum equation:
 solving an a priori simplified momentum equation: 
![\[ \rho^n \dfrac{(\vect{u}^{hydro} - \vect{u}^n)}{\Delta t} = \rho^n \vect{g}^n - \grad P_{hydro} \]](form_286.png) 
and using the mass equation as following:
![\[ \rho^n \divs \left( \delta \vect{u}_{hydro} \right) = 0 \]](form_287.png) 
 with: 
finally, we resolve the simplified momentum equation below:
![\[ \divs \left( K \grad P_{hydro} \right) = \divs \left(\vect{g}\right) \]](form_289.png) 
 with the diffusion coefficient (  ) defined as:
) defined as: 
![\[ K \equiv \dfrac{1}{\rho^n} \]](form_291.png) 
with a Neumann boundary condition on the hydrostatic pressure:
![\[ D_\fib \left( K, \, P_{hydro} \right) = \vect{g} \cdot \vect{n}_\ib \]](form_292.png) 
(see the theory guide for more details on the boundary condition formulation).
| subroutine prehyd | ( | double precision, dimension(ncelet) | prhyd, | 
| double precision, dimension(ncelet,ndim) | grdphd | ||
| ) | 
| [in,out] | prhyd | hydrostatic pressure predicted with the a priori momentum equation reduced   | 
| [out] | grdphd | the a priori hydrostatic pressure gradient   | 
 1.8.3.1
 1.8.3.1