Problem with Proper Orthogonal Decomposition of CFD data

Hi,

I am trying to apply POD (Proper Orthogonal Decomposition) using data from a Detached Eddy Simulation. I have the following pressure data at a point in the fluid domain:

when I run the following code that I have written I get a similar signal for the first mode but its values are too big when compared with original signal.

close; clear; clc; tic
X = load('X.dat'); 
P = [1 5 10 25 50 75 100 150 200]; 
F = 1; 
f = 1107; 
XMean = mean(X,2); 
[M,N] = size(X); 
XTilda = zeros(M,N); 
for i = 1:N
    XTilda(:,i) = X(:,i)-XMean; 
end
C = XTilda'*XTilda; 
[U,S,V] = svd(C); 
phi = XTilda*V; 
A = C*V; 
XHat = cell(length(P),1); 
Q = zeros(length(P),2); 
Q(:,1) = P; 
n = 0; 
for p = P
    n = n+1; 
    XHat{n} = zeros(M,N); 
    for i = 1:N
        sigma = 0; 
        for k = 1:P(n)
            sigma = sigma+A(i,k)*phi(:,k); 
        end
        XHat{n}(:,i) = XMean+sigma; 
    end
    Q(n,2) = 100*(sum(sum(S(:,1:P(n))))/sum(sum(S))); 
end
if isempty(F) == 0
    F1 = figure(1); 
    set(F1,'numbertitle','off')
    subplot(2,1,1)
    hold on
    plot(X(f,:),'.-k')
    n = 0; 
    for p = F
        n = n+1; 
        plot(XHat{n}(f,:),'.-')
    end
    ylabel('X')
    hold off
    subplot(2,1,2)
    plot(Q(:,1),Q(:,2),'.-')
    xlabel('P')
    ylabel('Q')
end
toc

I tried to find where I made a mistake and so far, I think I did good until the creation of the A matrix, and my Q graph shows the right trend for a POD analysis.

I'm thinking maybe I'm doing a mistake in the final loop.

I would appreciate any kind of help, thanks in advance.

Reference paper for the calculations: paper

Osman Mirza Demircan

[KSSV]

Did you check of the units if any....are in same system?

[Osman Mirza Demircan]

The pressure data are in pascals, I didn't check any units but I sticked to the procedure described in the reference paper that I shared at the end of the post.

[Thibault Clar]

Hi Osman, I am solving a similar problem, just wondering if you found out where your error was in the end?