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//
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2010-2010 - DIGITEO - Vincent LEJEUNE
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
//
//
//lines(0);
//abs_path=get_absolute_file_path("D2Q9.sce");
//exec(abs_path+"circshift.sce");
// %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
// % cylinder.m: Channel flow past a cylinderical
// % obstacle, using a LB method
// %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
// % Lattice Boltzmann sample in Matlab
// % Copyright (C) 2006-2008 Jonas Latt
// % Address: EPFL, 1015 Lausanne, Switzerland
// % E-mail: jonas@lbmethod.org
// % Get the most recent version of this file on LBMethod.org:
// % http://www.lbmethod.org/_media/numerics:cylinder.m
// %
// % Original implementaion of Zou/He boundary condition by
// % Adriano Sciacovelli (see example "cavity.m")
// %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
// % 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.
// %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
// Translated to scilab language by Vincent Lejeune
function D2Q9()
// GENERAL FLOW CONSTANTS
lx = 400; //number of cells in x-direction
ly = 100; // number of cells in y-direction
obst_x = lx/5+1; // position of the cylinder; (exact
obst_y = ly/2+3; // y-symmetry is avoided)
obst_r = ly/10+1; // radius of the cylinder
uMax = 0.1; // maximum velocity of Poiseuille inflow
Re = 100; // Reynolds number
nu = uMax * 2.*obst_r / Re; // kinematic viscosity
omega = 1. / (3*nu+1./2.); // relaxation parameter
maxT = 4; // total number of iterations
tPlot = 50; // cycles
// D2Q9 LATTICE CONSTANTS
t = [4/9, 1/9,1/9,1/9,1/9, 1/36,1/36,1/36,1/36];
cx = [ 0, 1, 0, -1, 0, 1, -1, -1, 1];
cy = [ 0, 0, 1, 0, -1, 1, 1, -1, -1];
opp = [ 1, 4, 5, 2, 3, 8, 9, 6, 7];
col = [2:(ly-1)];
in = 1; // position of inlet
out = lx; // position of outlet
// [y,x] = meshgrid(1:ly,1:lx); // get coordinate of matrix indices
// BJ : Alternative implementation to have C Code generation
y = ones(lx,1) * (1:ly);
x = (1:lx)' * ones(1,ly)
obst = ... // Location of cylinder
(x-obst_x).^2 + (y-obst_y).^2 <= obst_r.^2;
//obst(:,[1,ly]) = 1; // Location of top/bottom boundary
// BJ : alternative implementation
[obst_height, obst_width] = size(obst);
obst(1:obst_height,1) = 1; // Location of top/bottom boundary
obst(1:obst_height,ly) = 1; // Location of top/bottom boundary
bbRegion = find(obst); // Boolean mask for bounce-back cells
// INITIAL CONDITION: Poiseuille profile at equilibrium
L = ly-2; y_phys = y-1.5;
ux = 4 * uMax / (L*L) * (y_phys.*L-y_phys.*y_phys);
uy = zeros(lx,ly);
rho = 1;
fIn=zeros(9,lx,ly);
fEq=zeros(9,lx,ly);
fOut=zeros(9,lx,ly);
for i=1:9
cu = 3*(cx(i)*ux+cy(i)*uy);
fIn(i,:,:) = rho .* t(i) .* ...
( 1 + cu + 1/2*(cu.*cu) - 3/2*(ux.^2+uy.^2) );
end
//Matplot();
//f=gcf();
//f.color_map=jetcolormap(256);
// // MAIN LOOP (TIME CYCLES)
for cycle = 1:maxT
//
// // MACROSCOPIC VARIABLES
rho = sum(fIn,'m');
tmpx=cx*matrix(fIn,9,lx*ly);
tmpy=cy * matrix(fIn,9,lx*ly);
ux = matrix ( tmpx, 1,lx,ly) ./rho;
uy = matrix ( tmpy, 1,lx,ly) ./rho;
// MACROSCOPIC (DIRICHLET) BOUNDARY CONDITIONS
// Inlet: Poiseuille profile
y_phys = col-1.5;
ux(1,in,col) = 4 * uMax / (L*L) * (y_phys.*L-y_phys.*y_phys);
uy(1,in,col) = 0;
tmp=sum(fIn([1,3,5],in,col),'m') + 2*sum(fIn([4,7,8],in,col),'m');
rho(:,in,col) = ones(1,1,98) ./ (1-ux(:,in,col)) .* tmp;
// Outlet: Constant pressure
rho(:,out,col) = 1;
ux(:,out,col) = -ones(1,1,98) + ones(1,1,98) ./ (rho(:,out,col)) .* ( ...
sum(fIn([1,3,5],out,col),'m') + 2*sum(fIn([2,6,9],out,col),'m'));
uy(:,out,col) = 0;
// MICROSCOPIC BOUNDARY CONDITIONS: INLET (Zou/He BC)
fIn(2,in,col) = fIn(4,in,col) + 2/3*rho(:,in,col).*ux(:,in,col);
fIn(6,in,col) = fIn(8,in,col) + 1/2*(fIn(5,in,col)-fIn(3,in,col)) ...
+ 1/2*rho(:,in,col).*uy(:,in,col) ...
+ 1/6*rho(:,in,col).*ux(:,in,col);
fIn(9,in,col) = fIn(7,in,col) + 1/2*(fIn(3,in,col)-fIn(5,in,col)) ...
- 1/2*rho(:,in,col).*uy(:,in,col) ...
+ 1/6*rho(:,in,col).*ux(:,in,col);
// MICROSCOPIC BOUNDARY CONDITIONS: OUTLET (Zou/He BC)
fIn(4,out,col) = fIn(2,out,col) - 2/3*rho(:,out,col).*ux(:,out,col);
fIn(8,out,col) = fIn(6,out,col) + 1/2*(fIn(3,out,col)-fIn(5,out,col)) ...
- 1/2*rho(:,out,col).*uy(:,out,col) ...
- 1/6*rho(:,out,col).*ux(:,out,col);
fIn(7,out,col) = fIn(9,out,col) + 1/2*(fIn(5,out,col)-fIn(3,out,col)) ...
+ 1/2*rho(:,out,col).*uy(:,out,col) ...
- 1/6*rho(:,out,col).*ux(:,out,col);
// COLLISION STEP
for i=1:9
cu = 3*(cx(i)*ux+cy(i)*uy);
fEq(i,:,:) = rho .* t(i) .*( 1 + cu + 1/2*(cu.*cu) - 3/2*(ux.^2+uy.^2) );
fOut(i,:,:) = fIn(i,:,:) - omega .* (fIn(i,:,:)-fEq(i,:,:));
end
// OBSTACLE (BOUNCE-BACK)
for i=1:9
fOut(i,bbRegion) = fIn(opp(i),bbRegion);
end
// STREAMING STEP
for i=1:9
tmpmat=matrix(fOut(i,:,:),lx,ly);
tmp=cs(tmpmat,cx(i),cy(i));
fIn(i,:,:) = matrix(tmp,1,lx,ly);
end
//
// VISUALIZATION
//if (pmodulo(cycle,tPlot)==1)
u = matrix(sqrt(ux.^2+uy.^2),lx,ly);
u(bbRegion) = %nan;
//classe=linspace(0,1,1000);
//histplot(classe,u/max(u));
img=abs(255*u/max(u));
//disp(img);
//imshow(img');
//e=gce();
//e.data=img';
//xs2png(gcf(),'img-'+string(cycle)+'.png');
//imagesc(u');
//axis equal off; drawnow
// end
//tim=toc()
//disp(tim);
end
endfunction
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