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cavity_main_GSinter.m
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cavity_main_GSinter.m
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clc
clear
close all
%% physical properties
mu = 1e-2;
rho =1 ;
%% grid
dx = 0.02;
dr = 0.02;
nTubeAxis = 50;
nTubeRadius = 50;
n_points_x = nTubeAxis +1;
n_points_y = nTubeRadius +1;
%% boundary condition
uLeft = 0;
uRight = 0;
uTop = 1;
vBottom = 0;
vTop = 0;
%% initial u & v
u = 0*ones((nTubeAxis+1),nTubeRadius+2); % 11*7 unknown u points
u(:,nTubeRadius+2) = 2;
du = 0*u;
v = 0*ones(nTubeAxis+2,(nTubeRadius+1)); % 40 unknown v points
uGuess = u;
uNew = u;
vGuess = v;
vNew = v;
dv = v;
p = 0*ones(nTubeAxis+2,nTubeRadius+2); % 50 unknown p nodes
pCor = p;
b = pCor;
% cavity_initPressure
%% assign edge point (boundary number)
% cavity_uBoundaryNum;
% cavity_vBoundaryNum;
% cavity_pBoundaryNum;
%% initialize the coeff Mat and source Vec
uMat = zeros(numel(u),numel(u));
uVec = zeros(numel(u),1);
vMat = zeros(numel(v),numel(v));
vVec = zeros(numel(v),1);
pCorMat = zeros(numel(p),numel(p));
pCorVec = zeros(numel(p),1);
pNew = p;
iter = 0;
for exIter = 1:10000
%% construct uMat and uVec
for i = 2:n_points_x-1
for k = 2:n_points_y
j = 2+n_points_y-k;
Fe = dr * rho* (u(i,j) + u(i+1,j))/2;
Fw = dr * rho* (u(i,j) + u(i-1,j))/2;
Fs = dx * rho* (v(i,j-1) + v(i+1,j-1))/2;
Fn = dx * rho* (v(i,j) + v(i+1,j))/2;% n or s is a question
De = dr * mu/dx;
Dw = De;
Dn = dx * mu/dr;
Ds = Dn;
du(i,j) = dr/((Dw - Fw/2) + (De+Fe/2) + (Dn +Fn/2)+ (Ds - Fs/2));
uGuess(i,j) = (Dw + Fw/2)*u(i-1,j) + (De-Fe/2)*u(i+1,j) + (Dn -Fn/2)*u(i,j+1) + (Ds + Fs/2)*u(i,j-1);
uGuess(i,j) = uGuess(i,j)/((Dw - Fw/2) + (De+Fe/2) + (Dn +Fn/2)+ (Ds - Fs/2));
uGuess(i,j) = uGuess(i,j) + dr*(p(i,j)-p(i+1,j))/((Dw - Fw/2) + (De+Fe/2) + (Dn +Fn/2)+ (Ds - Fs/2));
end
end
uGuess(:,nTubeRadius+2) = 2-uGuess(:,nTubeRadius+1);
uGuess(:,1) = -uGuess(:,2);
uGuess(1,2:nTubeRadius+1) = 0;
uGuess(nTubeAxis+1,2:nTubeRadius+1) = 0;
%%
for i = 2:n_points_x
for k = 2:n_points_y-1
j = 2+n_points_y-1-k;
Fn = rho*dx*(v(i,j) + v(i,j+1))/2;
Fs = rho*dx*(v(i,j) + v(i,j-1))/2;
Fe = rho*dr*(u(i,j) + u(i,j+1))/2;
Fw = rho*dr*(u(i-1,j) + u(i-1,j+1))/2 ;
Dn = mu*dx/dr;
Ds = Dn;
De = mu*dr/dx;
Dw = De;
vGuess(i,j) = (Dw + Fw/2)*v(i-1,j) + (De -Fe/2)*v(i+1,j) + (Ds + Fs/2)*v(i,j-1) + (Dn - Fn/2)*v(i,j+1);
vGuess(i,j) = vGuess(i,j)/((Dw - Fw/2) + (De+Fe/2) + (Dn +Fn/2)+ (Ds - Fs/2));
vGuess(i,j) = vGuess(i,j) + dx*(p(i,j)-p(i,j+1))/((Dw - Fw/2) + (De+Fe/2) + (Dn +Fn/2)+ (Ds - Fs/2));
dv(i,j) = dx/((Dw - Fw/2) + (De+Fe/2) + (Dn +Fn/2)+ (Ds - Fs/2));
end
end
vGuess(1,:) = -vGuess(2,:);
vGuess(n_points_x+1,:) = -vGuess(n_points_x,:);
vGuess(2:n_points_x,1) = 0;
vGuess(2:n_points_x,n_points_y) = 0;
pCor = 0*pCor;%!!!!!!!!!!!!!!!!!!!!!!!cao 就是这玩意卡了我好久 气死！
for i=2:n_points_x
for k=2:n_points_y
j = n_points_y+2-k;
aE = rho*du(i,j)*dr;
aW = rho*du(i-1,j)*dr;
aN = rho*dv(i,j)*dx;
aS = rho*dv(i,j-1)*dx;
aP = aE+aW+aS+aN;
b(i,j) = rho*(dr*uGuess(i-1,j) - dr*uGuess(i,j) + dx*vGuess(i,j-1) - dx*vGuess(i,j) );
pCor(i,j) = (aE*pCor(i+1,j) + aW*pCor(i-1,j) + aN*pCor(i,j+1) + aS*pCor(i,j-1) +b(i,j))/aP;
end
end
for i =2:n_points_x
for j = 2:n_points_y
pNew(i,j) = pNew(i,j) + 0.8*pCor(i,j);
end
end
pNew(:,n_points_y+1) = pNew(:,n_points_y);
pNew(:,1) = pNew(:,2);
pNew(1,:) = pNew(2,:);
pNew(n_points_x+1,:) = pNew(n_points_x,:);
for i = 2:n_points_x-1
for j = 2:n_points_y+1
uNew(i,j) = uGuess(i,j) + 0.8*du(i,j)*(pCor(i,j)-pCor(i+1,j));
end
end
uNew(:,nTubeRadius+2) = 2-uNew(:,nTubeRadius+1);
uNew(:,1) = -uNew(:,2);
uNew(1,2:nTubeRadius+1) = 0;
uNew(nTubeAxis+1,2:nTubeRadius+1) = 0;
for i = 2:n_points_x
for j = 2:n_points_y-1
vNew(i,j) = vGuess(i,j) + 0.8*dv(i,j)*(pCor(i,j)-pCor(i,j+1));
end
end
vNew(1,:) = -vNew(2,:);% left
vNew(nTubeAxis+2,:) = -vNew(nTubeAxis+1,:);%right
vNew(2:nTubeAxis+1,1) = 0;
vNew(2:nTubeAxis+1,nTubeRadius+1) = 0;
error = 0;
for i = 2:n_points_x
for j = 2:n_points_y
error = error + abs(b(i,j));
end
end
u = uNew;
v = vNew;
p = pNew;
iter = iter +1;
if mod(iter,100)==0
contour(u(2:n_points_x,2:n_points_y));
drawnow
colorbar
error
% pause
end
if error < 1e-5
break
end
end