n_upwind.c

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/*****************************************************************************
 *
 * MODULE:       Grass PDE Numerical Library
 * AUTHOR(S):    Soeren Gebbert, Berlin (GER) Dec 2006
 *                 soerengebbert <at> gmx <dot> de
 *
 * PURPOSE:      upwinding stabilization algorithms
 *                 part of the gpde library
 *
 * COPYRIGHT:    (C) 2000 by the GRASS Development Team
 *
 *               This program is free software under the GNU General Public
 *               License (>=v2). Read the file COPYING that comes with GRASS
 *               for details.
 *
 *****************************************************************************/
 
#include <math.h>
#include <grass/N_pde.h>
 
/*! \brief full upwinding stabilization algorithm
 *
 * The arguments are values to compute the local peclet number
 *
 * \param sprod double -- the scalar product between the velocity vector and the
 * normal vector between two points \param distance double -- distance between
 * two points \param D double -- diffusion/dispersion tensor part between two
 * points
 *
 * \return the weighting factor
 * */
double N_full_upwinding(double sprod, double distance, double D)
{
    double z;
 
    if (D == 0)
        return 0.5;
 
    /*compute the local peclet number */
    z = sprod * distance / D;
 
    if (z > 0)
        return 1;
    if (z == 0)
        return 0.5;
    if (z < 0)
        return 0;
 
    return 0;
}
 
/*! \brief exponential upwinding stabilization algorithm
 *
 * The arguments are values to compute the local peclet number
 *
 * \param sprod double -- the scalar product between the velocity vector and the
 * normal vector between two points \param distance double -- distance between
 * two points \param D double -- diffusion/dispersion tensor part between two
 * points
 *
 * \return the weighting factor
 * */
double N_exp_upwinding(double sprod, double distance, double D)
{
    double z;
 
    if (D == 0)
        return 0.5;
 
    /*compute the local peclet number */
    z = sprod * distance / D;
 
    if (z != 0)
        return (1 - (1 / z) * (1 - (z / (exp(z) - 1))));
 
    return 0.5;
}