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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
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