8.1
general documentation
Functions/Subroutines
prehyd.f90 File Reference

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

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