Warning: Matrix is singular to working precision in one line

The code seems working perfectly fine but one line it gives an error and does not produce a graph as it should be, could someone explain the error in line 54

% 2-D Source Panel Method
% Reads panel points from a text file and calculates flow around the body.
% Clear workspace and command window
clear;
clc;
% Read panel points from a text file
filename = 'panel_points.txt';
panel_points = load(filename);

Error using load
Unable to find file or directory 'panel_points.txt'.

% Number of panels
N = size(panel_points, 1) - 1;
% Panel coordinates
x = panel_points(:, 1);
y = panel_points(:, 2);
% Prompt user for flow conditions
U_inf = input('Enter the free stream velocity (U_inf): ');
alpha = input('Enter the angle of attack (alpha in degrees): ');
alpha = deg2rad(alpha);
% Initialize matrices
A = zeros(N+1, N+1);
RHS = zeros(N+1, 1);
% Calculate panel lengths and angles
for i = 1:N
    x_mid(i) = 0.5 * (x(i) + x(i+1));
    y_mid(i) = 0.5 * (y(i) + y(i+1));
    s(i) = sqrt((x(i+1) - x(i))^2 + (y(i+1) - y(i))^2);
    theta(i) = atan2(y(i+1) - y(i), x(i+1) - x(i));
end
% Populate influence coefficient matrix
for i = 1:N
    for j = 1:N
        if i == j
            A(i,j) = 0.5;
        else
            A(i,j) = (1 / (2 * pi)) * log(sqrt((x_mid(i) - x(j))^2 + (y_mid(i) - y(j))^2) / sqrt((x_mid(i) - x(j+1))^2 + (y_mid(i) - y(j+1))^2));
        end
    end
    RHS(i) = -U_inf * cos(theta(i) - alpha);
end
% Apply Kutta condition
A(N+1,1) = 1;
A(N+1,N) = -1;
RHS(N+1) = 0;
% Solve for source strengths
LINE54 sigma = A \ RHS;
% Calculate tangential velocity and pressure coefficient
for i = 1:N
    V_t(i) = U_inf * sin(theta(i) - alpha) + sigma(i) - sigma(i+1);
    Cp(i) = 1 - (V_t(i) / U_inf)^2;
end
% Plotting the pressure coefficient distribution
figure;
plot(x_mid, Cp, '-o');
xlabel('x');
ylabel('C_p');
title('Pressure Coefficient Distribution');
set(gca, 'YDir', 'reverse');
grid on;
disp('Computation complete. Pressure coefficient distribution plotted.');

Enter the free stream velocity (U_inf): 30

Enter the angle of attack (alpha in degrees): 0

54 sigma = A \ RHS;

Warning: Matrix is singular to working precision.

> In untitled (line 54)

this is what I got and a blank graph

[Walter Roberson]

Please attach your data file.

Answer 1

[Matt Butts]

When the matrix is singular, the output of line 54 is an array of NaN values. Thus by the time you get to your plot, you have a bunch of NaNs which show up as blank since they don't contain any real values.

Address the issue with your matrix being singular and you should get a plot.