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/* 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
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