Matlab实现格子玻尔兹曼方法(Lattice Boltzmann Method,LBM)模拟
本帖最后由 VictorHugo 于 2020-3-11 14:56 编辑```
%LBM的matlab代码
%Matlab实现格子玻尔兹曼方法(Lattice Boltzmann Method,LBM)模拟
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% cylinder.m: Flow around a cyliner, using LBM
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% 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, MA02110-1301, USA.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear
% GENERAL FLOW CONSTANTS
lx = 250;
ly = 51;
obst_x = lx/5+1; % position of the cylinder; (exact
obst_y = ly/2+1; % y-symmetry is avoided)
obst_r = ly/10+1;% radius of the cylinder
uMax= 0.02; % 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 = 400000; % total number of iterations
tPlot= 5; % cycles
% D2Q9 LATTICE CONSTANTS
t= ;
cx = ;
cy = ;
opp = [ 1, 4,5,2,3, 8, 9, 6, 7];
col = ;
= meshgrid(1:ly,1:lx);
obst = (x-obst_x).^2 + (y-obst_y).^2 <= obst_r.^2;
obst(:,) = 1;
bbRegion = find(obst);
% INITIAL CONDITION: (rho=0, u=0) ==> fIn(i) = t(i)
fIn = reshape( t' * ones(1,lx*ly), 9, lx, ly);
% MAIN LOOP (TIME CYCLES)
for cycle = 1:maxT
% MACROSCOPIC VARIABLES
rho = sum(fIn);
ux= reshape ( ...
(cx * reshape(fIn,9,lx*ly)), 1,lx,ly) ./rho;
uy= reshape ( ...
(cy * reshape(fIn,9,lx*ly)), 1,lx,ly) ./rho;
% MACROSCOPIC (DIRICHLET) BOUNDARY CONDITIONS
% Inlet: Poiseuille profile
L = ly-2; y = col-1.5;
ux(:,1,col) = 4 * uMax / (L*L) * (y.*L-y.*y);
uy(:,1,col) = 0;
rho(:,1,col) = 1 ./ (1-ux(:,1,col)) .* ( ...
sum(fIn(,1,col)) + ...
2*sum(fIn(,1,col)) );
% Outlet: Zero gradient on rho/ux
rho(:,lx,col) = rho(:,lx-1,col);
uy(:,lx,col)= 0;
ux(:,lx,col)= ux(:,lx-1,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
% MICROSCOPIC BOUNDARY CONDITIONS
for i=1:9
% Left boundary
fOut(i,1,col) = fEq(i,1,col) + ...
18*t(i)*cx(i)*cy(i)* ( fIn(8,1,col) - ...
fIn(7,1,col)-fEq(8,1,col)+fEq(7,1,col) );
% Right boundary
fOut(i,lx,col) = fEq(i,lx,col) + ...
18*t(i)*cx(i)*cy(i)* ( fIn(6,lx,col) - ...
fIn(9,lx,col)-fEq(6,lx,col)+fEq(9,lx,col) );
% Bounce back region
fOut(i,bbRegion) = fIn(opp(i),bbRegion);
end
% STREAMING STEP
for i=1:9
fIn(i,:,:) = ...
circshift(fOut(i,:,:), );
end
% VISUALIZATION
if (mod(cycle,tPlot)==0)
u = reshape(sqrt(ux.^2+uy.^2),lx,ly);
u(bbRegion) = nan;
imagesc(u');
axis equal off; drawnow
end
end
``` 赞一个呀。 好厉害的样子，感觉稍微改改都能让本科生毕业了:lol
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