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+/*  This file is part of the OpenLB library
+ *
+ *  Copyright (C) 2015 Mathias J. Krause
+ *  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 FRINGE_2D_H
+#define FRINGE_2D_H
+
+#include<vector>    // for generic i/o
+#include<cmath>     // for lpnorm
+
+#include "analyticalF.h"
+#include "io/ostreamManager.h"
+
+/** A fringe zone is a spatial domain, which is included into the
+ *  computational domain to aim a transition from turbulent into
+ * laminar flow. It is often applied to improve the use of
+ * artificial boundary conditions.
+ *
+ *                 lambda_max
+ *               _____________
+ *              /             \
+ *             /               \
+ *            /                 \
+ *           /                   \
+ *          /                     \
+ * ________/                       \________
+ *         |x_start                | x_ende
+ *         |-----|           |-----|
+ *             b_rise         b_fall
+ *
+ * fringe function:
+ *   lambda(x) = lambda_max*[S((x-x_start)/(b_rise)) - S((x-x_end)/(b_fall)+1)]
+ * The fringe function sets the strength of the damping. The
+ * maximum strength is lambda_max and the shape of the function is defined by
+ * the stepfunction S(x) and the parameters b_rise and b_fall.
+ *
+ * lambda_max: maximal damping force
+ * x_start: begin of the fringe zone
+ * x_end: end of the fringe zone
+ * b_rise: rise distance
+ * b_fall: fall distance
+ *
+ * S is a smooth step function:
+ * S(x)=0,     for x<=0
+ * S(x)=1/( 1 + exp( (1/(x-1)) + (1/x) ) ),  for 0<x<1,
+ * S(x)=1,     for x>=1.
+ *
+ * --> G = lambda*(U - u) is the volume force, which is added to
+ * the flow equations in order to transfer the actual velocity into the wanted
+ * velocity field
+ *
+ * u: actual velocity
+ * U: wanted velocity - either average profil or poiseuille profile
+ *
+ * BibteX listing of the main paper:
+ *
+ * @TECHREPORT{lundbladh:99,
+ *   author = {Anders Lundbladh and Stellan Berlin and Martin
+ *             Skote and Casper Hildings and Jaisig Choi and
+ *             John Kim and Dan Henningson},
+ *   title = {An Efficient Spectral Method for Simulation of
+ *            Incompressible Flow Over a Flat Plate},
+ *   institution = {not set},
+ *   url = {http://www.fluidosol.se/thesismod/paper9.pdf},
+ *   year = {1999} }
+ */
+
+
+namespace olb {
+
+template <typename T, typename S>
+class Fringe2D : public AnalyticalF2D<T,S> {
+
+private:
+  /// Wanted lattice velocity (in lattice units)
+  AnalyticalF2D<T,S>& _wantedVelocity;
+  /// Start of the fringe zone in _direction in physR (Si units)
+  T _start;
+  /// End of the fringe zone in _direction in physR (Si units)
+  T _end;
+  /// Direction of the fringe zone (parallel to x-axis means _direction = 0, parallel to y-axis means _direction = 1)
+  int _direction;
+  /// Maximum damping (TODO physical? depent on dt?)
+  T _lambdaMax;
+  /// Percentage of the length of the fringezone at the beginning, aim: softer increase of lambda
+  T _rise;
+  /// Percentage of the length of the fringezone at the end
+  T _fall;
+
+public:
+  Fringe2D(AnalyticalF2D<T,S>& wantedVelocity, T start, T end, int direction, T lambdaMax=.005, T rise=.4, T fall=.2);
+
+  /// Returns coefficients (a1, a2, B11, B12, B21, B22)
+  /// for a linear velocity force modell where F = a + B*lattticeVelocity
+  /// a = -scaleLambda*wanted, B = (scaleLamda 0 0 scaleLamda), so that
+  /// F = scaleLambda*(latticeVelocity - wantedVelocity)
+  bool operator()(T output[6], const S input[2]);
+
+private:
+  /// Step function
+  T s(const T& x) const;
+  /// Damping function
+  T lambda(const T& x) const;
+};
+
+} // end namespace olb
+
+#endif
+
+