/*  This file is part of the OpenLB library
 *
 *  Copyright (C) 2006, 2007 Jonas Latt
 *  E-mail contact: info@openlb.net
 *  The most recent release of OpenLB can be downloaded at
 *  <http://www.openlb.net/>
 *
 *  This program is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU General Public License
 *  as published by the Free Software Foundation; either version 2
 *  of the License, or (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public
 *  License along with this program; if not, write to the Free
 *  Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
 *  Boston, MA  02110-1301, USA.
*/

#ifndef FINITE_DIFFERENCE_H
#define FINITE_DIFFERENCE_H

namespace olb {

namespace fd {

/// Second-order central gradient (u_p1 = u(x+1))
template<typename T>
T centralGradient(T u_p1, T u_m1)
{
  return (u_p1 - u_m1) / (T)2;
}

/// Second-order asymmetric gradient (u_1 = u(x+1))
template<typename T>
T boundaryGradient(T u_0, T u_1, T u_2)
{
  return (-(T)3*u_0 + (T)4*u_1 - (T)1*u_2) / (T)2;
}

/// Forward second-order first derivative
template<typename T>
T FSGradient(T u_0, T u_1, T u_2)
{
  T result = boundaryGradient(u_0, u_1, u_2);
  return result;
}

/// Backward second-order first derivative
template<typename T>
T BSGradient(T u_0, T u_1, T u_2)
{
  T result = -1*boundaryGradient(u_0, u_1, u_2);
  return result;
}

/// Value at u_0 for which asymmetric gradient is zero (u_1 = u(x+1))
template<typename T>
T boundaryZeroGradient(T u_1, T u_2)
{
  return (T)4/(T)3*u_1 - (T)1/(T)3*u_2;
}

/// Linear interpolation (yields u0 at pos=0 and u1 at pos=1)
template<typename T>
T linearInterpolate(T u_0, T u_1, T pos)
{
  return ((T)1-pos)*u_0 + pos*u_1;
}

}  // namespace fd

}  // namespace olb


#endif