# Errors trying to get the right plots

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Cesar Cardenas on 29 Mar 2023
Commented: VBBV on 30 Mar 2023
I'm trying to get the plots shown in the enclosed image. Not sure how to fix the code. Attached the .txt data file. Any help will be appreciated. Thanks
close all
clear all
clc
% Inputs
A = 10;
m = 0.06;
L = 1;
nu = 2e-5; % Kinematic viscosity of the fluid
rho = 10; % Fluid density
x_start = 0.2;
x_end = 1;
dx = 0.001;
y_start = 0;
y_high = round(max(VelN(:,1)),2);
y_end = y_high;
dy = 0.0001;
N = (x_end - x_start) / dx + 1
N = 801
M = (y_end - y_start) / dy + 1
M = 501
Re_x = A * L / nu;
% Initialize arrays
U = zeros(M, N);
Ue = zeros(1, N);
Theta = zeros(1, N);
cf = zeros(1, N);
y = linspace(y_start, y_end, M);
x = linspace(x_start, x_end, N);
%Inital Data Interpolation
Uef = @(XX)A*(XX/L).^m;
u = interp1(VelN(:,1),VelN(:,2),y)*Uef(x_start);
% Boundary conditions
U(1, :) = 0;
U(M, :) = 1;
% Solve for velocity profile using an explicit finite method
for i = 1:N
Ue(i) = (x(i) / L)^m * A;
theta = zeros(1, M);
for j = 2:M-1
F = [U(j-1, i), U(j, i), U(j+1, i)];
Uy = (F(3) - F(1)) / (2 * dy);
Uyy = (F(3) - 2 * F(2) + F(1)) / dy^2;
theta(j) = theta(j-1) + U(j, i) * dy / Ue(i);
cf(i) = 2 * nu * Uy / Ue(i)^2;
U(j, i+1) = U(j, i) + (U(j, i) * (F(3) - F(1)) - U(j, i)^2 * theta(j) + nu * Uyy) * dx / Ue(i)^2;
end
Theta(i) = trapz(y, 1 - U(:, i));
end
% Plot results
figure
plot(x, Theta,'o-')
title('Momentum thickness as a function of x')
xlabel('x')
ylabel('\theta')
figure
semilogy(x, cf,'o-')
title('Skin friction coefficient as a function of x')
xlabel('x')
ylabel('C_f')
% figure
% plot(y,u)
%
% title('Velocity Profile')
% xlabel('u [m/s]')
% ylabel('y [mm]')
%axis([-.001 .05 0 y_end])
figure
for i = 1:100:N
plot(U(:, i), y,'-')
hold on
end
title('Velocity profiles')
xlabel('u [m/s]')
ylabel('y [mm]')
%axis([-.001 .05 0 y_end])
legend('x = 0.2 m', 'x = 0.3 m', 'x = 0.4 m', 'x = 0.5 m', 'x = 0.6 m', 'x = 0.7 m', 'x = 0.8 m', 'x = 0.9 m', 'x = 1.0 m')
figure
for i = 1:100:N
U_over_Ue = U(:, i) / Ue(i);
y_over_theta = y / Theta(i);
plot(U_over_Ue, y_over_theta,'o-')
hold on
end
title('Velocity profiles normalized by momentum thickness')
xlabel('u/U_e')
ylabel('y/\theta')
axis([-0.001 .125 0 1.01])
legend('x = 0.2 m', 'x = 0.3 m', 'x = 0.4 m', 'x = 0.5 m', 'x = 0.6 m', 'x = 0.7 m', 'x = 0.8 m', 'x = 0.9 m', 'x = 1.0 m')
Cesar Cardenas on 29 Mar 2023
Ok thank you, however, I have not been able to get the plots as shown in the image attached, so not sure how to fix it.?
VBBV on 30 Mar 2023
When vector U are all zeros, its less likely, that velocity profile can be evaluated correctly,
There needs to be a condition where the vector U needs to be updated with right values
theta(j) = theta(j-1) + U(j, i) * dy / Ue(i);
% ------------------->>> theta vector are all zeros, conisder u(j) or some
% input taken from VelN variable or combination of both u(j) & VelN
% Recheck whether this equation is correctly formulated
U(j, i+1) = U(j, i) + (U(j, i) * (F(3) - F(1)) - U(j, i)^2 * theta(j) + nu * Uyy) * dx / Ue(i)^2;