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point_gauss.m
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point_gauss.m
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mat=zeros(2000,200);
value=zeros(1,2000);
disp('steady state heat conduction problem');
m=input('enter the number of nodes in the x direction');
n=input('enter the number of nodes in y direction');
t1=input('enter the temperature of left wall');
t2=input('enter the temperature of right wall');
t3=input('enter the temperature of bottom wall');
t4=input('enter the temperature of top wall');
if m==''
m=20;
elseif n==''
n=20;
elseif t1==''
t1=300;
elseif t2==''
t2=100;
elseif t3==''
t3=400;
elseif t4==''
t4=200;
end
t=zeros(m,n);
t_old=zeros(m*n,1);
t_new=zeros(m*n,1);
deltax=1/m;
deltay=1/n;
w1=1/(deltax*deltax);
w2=1/(deltay*deltay);
for i=1:m
for j=1:n
if i==1
if j==1
ap=-3*(w1+w2);
ae=w1;
an=w2;
s=2*t1*w1+2*t3*w2;
value(1)=-s;
for k=1:m
for l=1:n
if k==1 && l==1
mat(1,1)=ap;
elseif k==2 && l==1
mat(1,n+1)=an;
elseif k==1 && l==2
mat(1,2)=ae;
end
end
end
elseif j==n
ap=-3*(w1+w2);
aw=w1;
an=w2;
s=2*t2*w1+2*t3*w2;
value(j)=-s;
for k=1:m
for l=1:n
if k==1 && l==n
mat(n,n)=ap;
elseif k==1 && l==n-1
mat(n,n-1)=aw;
elseif k==2 && l==n
mat(n,2*n)=an;
end
end
end
else
ap=-(2*w1+3*w2);
s=2*t3*w2;
ae=w1;
aw=w1;
an=w2;
value(j)=-s;
for k=1:m
for l=1:n
if k==1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=ap;
elseif k==1 && l==j-1
mat(j+(i-1)*n,l+(k-1)*n)=aw;
elseif k==1 && l==j+1
mat(j+(i-1)*n,l+(k-1)*n)=ae;
elseif k==2 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=an;
end
end
end
end
elseif i==m
if j==1
ap=-3*(w2+w1);
as=w2;
ae=w1;
s=2*(t1*w1+t4*w2);
value(j+(i-1)*n)=-s;
for k=1:m
for l=1:n
if k==m && l==1
mat(j+(i-1)*n,l+(k-1)*n)=ap;
elseif k==m-1 && l==1
mat(j+(i-1)*n,l+(k-1)*n)=as;
elseif k==m && l==2
mat(j+(i-1)*n,l+(k-1)*n)=ae;
end
end
end
elseif j==n
ap=-3*(w2+w1);
as=w2;
aw=w1;
s=2*(t2*w1+t4*w2);
value(j+(i-1)*n)=-s;
for k=1:m
for l=1:n
if k==m && l==n
mat(j+(i-1)*n,l+(k-1)*n)=ap;
elseif k==m && l==n-1
mat(j+(i-1)*n,l+(k-1)*n)=aw;
elseif k==m-1 && l==n
mat(j+(i-1)*n,l+(k-1)*n)=as;
end
end
end
else
ap=-(2*w1+3*w2);
s=2*w2*t4;
ae=w1;
aw=w2;
value(j+(i-1)*n)=-s;
for k=1:m
for l=1:n
if k==m && l==j
mat(j+(i-1)*n,l+(k-1)*n)=ap;
elseif k==m-1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=as;
elseif k==m && l==j-1
mat(j+(i-1)*n,l+(k-1)*n)=aw;
elseif k==m && l==j+1
mat(j+(i-1)*n,l+(k-1)*n)=ae;
end
end
end
end
elseif j==1
if i~=1 && i~=m
ap=-(3*w1+2*w2);
s=2*t1*w1;
ae=w1;
an=w2;
as=w2;
value(j+(i-1)*n)=-s;
for k=1:m
for l=1:m
if k==i && l==j
mat(j+(i-1)*n,l+(k-1)*n)=ap;
elseif k==i-1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=as;
elseif k==i+1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=an;
elseif k==i && l==j+1
mat(j+(i-1)*n,l+(k-1)*n)=ae;
end
end
end
end
elseif j==n
if i~=1 && i~=m
ap=-(3*w1+2*w2);
s=2*t2*w1;
aw=w1;
an=w2;
as=w2;
value(j+(i-1)*n)=-s;
for k=1:m
for l=1:n
if k==i && l==j
mat(j+(i-1)*n,l+(k-1)*n)=ap;
elseif k==i-1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=as;
elseif k==i+1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=an;
elseif k==i && l==j-1
mat(j+(i-1)*n,l+(k-1)*n)=aw;
end
end
end
end
else
ap=-2*(w1+w2);
ae=w1;
aw=w1;
an=w2;
as=w2;
s=0.0;
value(j+(i-1)*n)=-s;
for k=1:m
for l=1:n
if k==i && l==j
mat(j+(i-1)*n,l+(k-1)*n)=ap;
elseif k==i-1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=as;
elseif k==i+1 && l==j
mat(j+(i-1)*n,l+(k-1)*n)=an;
elseif k==i && l==j-1
mat(j+(i-1)*n,l+(k-1)*n)=aw;
elseif k==i && l==j+1
mat(j+(i-1)*n,l+(k-1)*n)=ae;
end
end
end
end
end
end
iter=0;
for i=1:m
for j=1:n
t_old(j+(i-1)*n,1)=min(t1,t3); %temperature at all nodal points is initialised
end
end
diff=40;
n_d=1;
while diff>1e-01
iter=n_d;
for i=1:m*n
sum=0.0;
if i==1
iter=1*n;
for k=1:m*n
if k~=i
sum=sum+mat(i,k)*t_old(k);
end
end
t_new(i)=(value(i)-sum)/mat(1,1);
diff=abs(t_old(1)-t_new(1));
t_old(1)=t_new(1);
else
for k=1:m*n
if k~=i
sum=sum+mat(i,k)*t_old(k);
end
end
t_new(i)=(value(i)-1*sum)/mat(i,i);
end
diff1=abs(t_old(i)-t_new(i));
t_old(i)=t_new(i);
diff=max(diff,diff1);
end
n_d=n_d+1;
end
for s=1:m
for q=1:n
t(s,q)=t_new(q+(s-1)*n);
end
end
[x,y]=meshgrid(1:m,1:n);
contourf(x,y,t);
colorbar;