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| %1.Define data
%1.0.Simple data
rho=1000;
g=9.8;
mu=0.001;
eps=0.001;
NN=9;
NE=14;
error=0.0001;
%1.1.Conectivity matrix
E= [1 -1 0 0 0 0 0 0 0;
1 0 -1 0 0 0 0 0 0;
1 0 0 -1 0 0 0 0 0;
0 1 0 -1 0 0 0 0 0;
0 1 0 0 -1 0 0 0 0;
0 0 1 0 0 -1 0 0 0;
0 0 0 1 0 -1 0 0 0;
0 0 0 1 -1 0 0 0 0;
0 0 1 0 0 0 -1 0 0;
0 0 0 0 0 1 -1 0 0;
0 0 0 0 0 1 0 -1 0;
0 0 0 0 0 0 1 -1 0;
0 0 0 0 0 0 0 1 -1;
0 0 0 1 0 0 0 0 -1];
%1.2.Lengths vector
L=[600;400;900;400;400;350;600;400;300;500;300;350;600;300];
%1.3.Diameters vector
D=[0.5;0.5;0.5;0.5;0.4;0.5;0.5;0.4;0.3;0.3;0.3;0.3;0.3;0.3];
%1.4.Inflows at the nodes vector. The unknown inflows will be set to zero
%initially, and then will change its value (C2, C3, C5)
C=[-0.2;0;0;0;0;0;0;-0.5;-0.3];
%1.5.Piezometric heights vector.
H=[0;200;200;0;500;0;0;0;0];
%1.6.Boolean vector that determines whether we know the inflow Ci or the
%piezometric height Hi (1 for known C and 0 for known H)
BOOL=[1;0;0;1;0;1;1;1;1];
%1.7.Valves f vector
F=[0;0;0;0;10;0;0;15;0;0;0;0;10;0];
%1.8.Initialise Q vector
Q=ones(NE,1);
%1.9.Initialise Lambdas vector
LA=zeros(NE,1);
for i=1:NE
LA(i)=(-2*log(eps/(D(i)*3.7))/log(10))^-2;
end
%2.Problem solution
BOOL2=1;
iteration=1;
RELQ=zeros(NE,100000);
RELX=zeros(NE,100000);
MEMX=zeros(NN,100000);
MEMQ=[Q,zeros(NE,100000-1)];
RESIDUALS=zeros(NE,100000);
while BOOL2==1
%2.1.Define K matrix (diagonal, such that E*H=K*Q)
K=diag([zeros(1,NE)]);
for i=1:NE
K(i,i)=8*abs(Q(i))*(LA(i)*L(i)/D(i)+F(i))/(g*pi^2*D(i)^4);
end
%Calculate residuals for the problem (from the previous iteration
RESIDUALS(:,iteration)=abs(Q-((K\E)*H));
%2.2.Define M matrix as tras(E)*inv(K)*E
M=E'*(K\E);
%2.3.Use of the algorithm (shown in class) to find the A matrix.
A=zeros(NN,NN);
for j=1:NN
%Known C(j)
if BOOL(j)==1
for i=1:NN
A(i,j)=M(i,j);
end
%Known H(j)
else
for i=1:NN
if i==j
A(i,j)=-1;
end
end
end
end
%2.4.Use of the algorithm to find b vector
b=zeros(NN,1);
for i=1:NN
for j=1:NN
b(i)=b(i)-M(i,j)*(H(j)*(1-BOOL(j)));
end
if BOOL(i)==1
b(i)=b(i)+C(i);
end
end
%Solve the system of equations A*x=b
x=A\b;
%Set the values of x into the correspondent vector (either H or C)
for i=1:NN
if BOOL(i)==1
H(i)=x(i);
else
C(i)=x(i);
end
end
%Compute Q
Q=K\E*H;
%Store values of Q and X in two matrices
for i=1:NE
MEMQ(i,iteration+1)=Q(i);
end
for i=1:NN
MEMX(i,iteration+1)=x(i);
end
%Calculate relative increments for Q and X
for i=1:NE
RELQ(i,iteration)=abs((MEMQ(i,iteration+1)-MEMQ(i,iteration))/MEMQ(i,iteration+1));
end
for i=1:NN
RELX(i,iteration)=abs((MEMX(i,iteration+1)-MEMX(i,iteration))/MEMX(i,iteration+1));
end
%Compare relative increments and residuals with the error limit
BOOL2=0;
if max(RELQ(:,iteration))>=error
BOOL2=1;
end
if max(RELX(:,iteration))>=error
BOOL2=1;
end
if max(RESIDUALS(:,iteration))>=error
BOOL2=1;
end
%Recalculate lambda before next iteration
RE=zeros(NE,1);
for i=1:NE
RE(i)=4*rho*abs(Q(i))/(pi*mu*D(i));
end
for j=1:10
for i=1:NE
LA(i)=(-2*log((eps/(D(i)*3.7))+(2.51/(RE(i)*sqrt(LA(i)))))/log(10))^-2;
end
end
iteration=iteration+1;
if (iteration==100000)
BOOL2=0;
end
end
PLOT1=zeros(iteration,1);
PLOT2=zeros(iteration,1);
PLOT3=zeros(iteration,1);
for i=1:iteration
PLOT1(i)=max(RELQ(:,i));
PLOT2(i)=max(RELX(:,i));
PLOT3(i)=max(RESIDUALS(:,i));
end
semilogy(PLOT1)
semilogy(PLOT2)
semilogy(PLOT3) |
