I am trying to plot the change in u (diff_u) agaist the iteration to prove that diff_u converges. What is the best way to do this?

Below is my code, with z being the iteration counter:

`%% Parameters`

rho = 1.225; % kg/m^3 - Air sea level standard day

U = 10; % m/s - freestream

mu = 1.789e-5; % kg/(m*s) - Air sea level standard day

nu = mu/rho; % m^2/s

L = 0.25; % m

H = 0.05; % m % nx and ny defines matrix grid, dx and dy for step size

nx = 50;ny = 10;dx = .005; % 50 grid points in x-dir - .005m spacing

dy = .005; % 10 grid points in y-dir - .005m spacing

% Re based on length

Re_L = U*L/nu; % Filling mesh with 0 to begin

v = zeros(ny,nx); % All initial v are 0

u = ones(ny,nx)*U; % Filling the entire mesh with all u = 10

% Boundary Conditions

% Goes (j,i) each segment, fills mesh with known values

u(:,1) = U; % Inlet

v(:,1) = 0; % Inletu(1,:) = 0; % No Slip wall

v(1,:) = 0; % No Slip wallu(ny,:) = U; % Free stream (top of mesh)

%% Solving

% Guess values of alpha

alphau = 0.001; %guess, will need to figure out best value for this

alphav = 0.1; % Differences

diff_u=[];diff_v=[];diff_u_max=[];diff_v_max=[];diff_both=[]; % Tolerance and convergence for main while loop

tol = .001;converge = false;z = 0; % Starting the index for iterations

while z < 20 % This is number of iterations it performs

z = z + 1; for j = 2:1:ny-1 for i = 2:1:nx-1 u_i = u(j,i+1); u(j,i+1) = (2*dx/u(j,i)) * (((mu/rho)*((u(j-1,i) + 2*u(j,i) + u(j+1,i))/(dy^2))) - (v(j,i)*((u(j-1,i) - u(j+1,i))/(2*dy)))) + u(j,i-1); change_u = u_i - u(j,i+1); u(j,i+1) = u_i + (alphau * change_u); v_j = v(j+1,i); v(j,i+1) = v(j-1,i+1) - dy/2/dx*(u(j,i+1)-u(j,i)+u(j-1,i+1)-u(j-1,i)); change_v = v_j - v(j,i+1); v(j,i+1)= v_j + (alphav * change_v); diff_u = [diff_u change_u]; diff_v = [diff_v change_v]; end end diff_U = max(abs(diff_u)) diff_V = max(abs(diff_v)) diff_u_max = [diff_u_max diff_U]; diff_v_max = [diff_v_max diff_V]; diff = [diff_U diff_V]; max_diff = max(diff); %if max_diff < tol

% z = 0; % I dont think this is right. Want max_diff < tol then iterations = 0 so it stops iterating

%end

% WANT TO PLOT THE CHANGE IN u TO SHOW IT CONVERGES

end

## Best Answer