Can't complete contour fill graph

I'm trying to plot this contour graph predicting melt pool dimensions at different laser power (P) and scan speed (u), and I want the y axis to start at P = 0.5. The problem is, I can't get g (aka the z value) high enough to make that possible. For each combination of P and u, we get a specific value of g2, which is the level I use to find the melt pool dimensions from. The lower the P value, the higher the g2 value. The lowest P I can use is around 40. I've tried adjusting the mesh size (basically zooming in) and no dice. Is there a way to interpolate the data or something so I can include y = 0.5? I've included a picture of what the graph should look like.

Also, since my description probably doesn't make sense without the code, here's what I've got so far:

clear all
close all
clc
%Constant
rho = 4420;          %kg/m^3
Cp = 550;            %J/kg?K
T0 = 303.15;         %K
A = 0.5;             %[Absorbtivity] 
k = 7.2;             %W/m/K
alpha = 2.96*10^-6;  %m^2/s
D = alpha;
P = 100;             %W
v = 1;               %m/s
u = v;
Tm = 1933;        %K
d_laser = 0.0001;    %m
r_laser = d_laser/2; %m
a = r_laser;
p = D/(u*a);
%Define
n = 100;
x = linspace(-0.00025,0.00125,n);
y = linspace(-0.00025,0.00025,n);
z = linspace(0,0.0005,n);
%Normalized
x_nor = x/a;
y_nor = y/a;
z_nor = z/(D*a/u).^0.5;
%Mesh grid
[x_mesh,y_mesh] = meshgrid(x_nor,y_nor)
z = 0;

% Specify the range of P and u
n = 4
P_range = [50 100 200 300 400]
u_range = [0.5 1 2 3 4] 
num_P = length(P_range);
num_u = length(u_range);
melt_pool_length = zeros(num_u, num_P);
melt_pool_width = zeros(num_u, num_P);
melt_pool_depth = zeros(num_u, num_P);


% Calculate melt pool dimensions for different values of P and u
for i = 1:num_u
    for j = 1:num_P
        u = u_range(i)
        P = P_range(j)
        % Calculate g for each P and u
       fun = @(t) exp((-z^2./(4*t))-((y_mesh.^2+(x_mesh-t).^2)./(4*p.*t+1)))./((4.*p.*t+1).*sqrt(t));
        g = integral(fun,0,Inf,'ArrayValued',true);
        Ts = (0.5*P)/(pi*rho*Cp*sqrt(D*u*(a^3)))
        % Find the contour level where g is equal to the ratio
         g2 = Tm/Ts
          contourc(x, y, g) 
      %ind=find(c2(1,:)==max(c_lev)-1);
        contourdata = contourc(x_nor, y_nor, g, [g2 g2]) 
          
        % Initialize arrays to store the boundary coordinates
        x_prime = [contourdata(1,2:size(contourdata,2))]
        y_prime = [contourdata(2,2:size(contourdata,2))]

        % Calculate melt pool dimensions using the extracted boundary coordinates
        melt_pool_length(i, j) = max(x_prime) - min(x_prime)
        melt_pool_width(i, j) = max(y_prime) - min(y_prime)
      
    end
end

[u_mesh,P_mesh]=meshgrid(u_range,P_range)
transpose(u_mesh)
transpose(P_mesh)
melt_pool_width = melt_pool_width.*10^6.*a
melt_pool_length = melt_pool_length .* 10^6.*a

figure;
levelindex = [90 120 150 180 210 240]
 [A,B] = contourf(transpose(u_mesh), transpose(P_mesh), melt_pool_width, levelindex, Color='white');
clabel(A,B,'Color','white')
colorbar;
xlabel('Scanning velocity (m/s)');
ylabel('Laser power (W)');
title('Melt Pool Width (\mum)');

%Plot the contour graph of melt pool dimensions
figure;
contourf(transpose(u_mesh), transpose(P_mesh), melt_pool_length, Color='white');
colorbar;
xlabel('Scanning velocity (m/s)');
ylabel('Laser power (W)');
title('Melt Pool Length');

[Mathieu NOE]

according to your image , P starts around 50 and not 0.5 (confusion with u lower limit ?)

so your code has the right min / max u and P limits

but if your code generate another result vs what you expected this maybe comes from another issue

Answer 1

[Brahmadev]

Hi @Sarinya,

For interpolating Interpolation for 2-D gridded data in meshgrid format, the 'interp2' function can be used. See example below.

% create an extended range for P values
P_range_ext = [0.5 40 50 100 200 300 400]

% Create an extended meshgrid using the "meshgrid" function
[u_mesh_ext,P_mesh_ext]=meshgrid(u_range,P_range_ext)

% Extrapolate the data using the "interp2" function
melt_pool_width_ext = interp2(u_mesh,P_mesh,melt_pool_width,u_mesh_ext,P_mesh_ext,'makima');

Further, ther data can be normalized according as per need and a contour can be plotted using 'contourf' function.

You can see the MathWorks documentation for the 'interp2' using the following link: https://www.mathworks.com/help/matlab/ref/interp2.html

Hope this helps in resolving your query!