%By liu-2017.0403. 谢谢这位没写名字的大佬。
%又上网扒代码了。基础太差，不看看大佬们的杰作是要把小的愁死啊~
%一样感人的效果。然而还不清楚这个是撒。。等我啃一啃再更新哈
%还是老样子，有啥问题Feel free to tell us~毕竟群众力量大嘛~QQ群：293267908。
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear
% GENERAL FLOW CONSTANTS
lx = 250;
ly = 250;
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 = 0.06; % 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 = 4000; % total number of iterations
tPlot = 5; % 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)];
[y,x] = meshgrid(1:ly,1:lx);
% obst = (x-obst_x).^2 + (y-obst_y).^2 <= obst_r.^2;
obst = (abs(y-4.*(x-110)-50)<=1.8).*(x>=110).*(x<=120)+...
(abs(y+4.*(x-140)-50)<=1.8).*(x>=130).*(x<=140);
% obst = zeros(lx,ly);
obst([1,lx],:) = 1;
obst(:,ly) =1 ;
obst([1:110],1)=1;
obst([140:250],1)=1;
obst(110,[1:50])=1;
obst(140,[1:50])=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(:,[111:139],1) = 0;
uy(:,[111:139],1) = uMax;
rho(:,[111:139],1) = 1 ./ (1-uy(:,[111:139],1)) .* ( ...
sum(fIn([1,4,2],[111:139],1)) + ...
2*sum(fIn([5,8,9],[111:139],1)));
% % 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(7,1,col) - ...
fIn(6,1,col)-fEq(7,1,col)+fEq(6,1,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,:,:), [0,cx(i),cy(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