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Falkner-Skan code

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Cesar Cardenas
Cesar Cardenas on 26 Mar 2023
Answered: John D'Errico on 26 Mar 2023
Hello, I would like to know how to include or implement this equation:
tau = (mu/(2*delta_y))*(4*un,2-un,3)
into this code:? Any help will be greatly appreciated. I'm really stuck.
function BLSolver(xstart,xend,delta_x, ...
Ny,ymax,A,m,nu,L)
% Inputs
% xstart: starting location (m)
% xend: ending location (m)
% delta_x: x step size (m)
% Ny: number of points in the wall-normal direction
% ymax: maximum value of wall-normal coordinate (m)
% A, m, L: constants for Falkner-Skan edge velocity distribution, Ue =
% A(x/L)^m
% nu: kinematic viscosity (m^2/s)
% Create a vector of x locations, where we will solve for the boundary
% layer profiles.
x = (xstart:delta_x:xend)';
Nx = length(x);
% Calculate the edge velocity
Ue = A*(x/L).^m;
% Initialize variables
u = zeros(Ny,1);
v = zeros(Ny,1);
u_ns = u; v_ns = v;
% Calculate the y points and the y spacing
y = linspace(0,ymax,Ny)';
delta_y = y(2)-y(1);
% Initialize skin friction coefficient, momentum thickness vectors
theta = zeros(Nx,1);
cf = zeros(Nx,1);
% Initialize Solution at xstart by loading the starting profile
% ENTER CODE HERE %
u = ...
v = ...
% Calculate theta, cf for initial profile
% ENTER CODE HERE %
theta(1) = ...
cf(1) = ...
% Start Finite Difference Solution
for LCVx = 2:Nx
% Toggle display for troubleshooting
% disp(['Calculating Streamwise Position ' ...
% num2str(LCVx) ' of ' num2str(Nx) ' (x = ' ...
% num2str(x(LCVx)) ' m)'])
% Solve for u at the next x location
% ENTER CODE HERE %
u_ns = ...
% Solve for v at the next x location using the continuity equation
% ENTER CODE HERE %
v_ns = ...
% Update velocity profiles
u = u_ns;
v = v_ns;
% Calculate momentum thickness
% ENTER CODE HERE %
theta(LCV) = ...
% Calculate skin friction coefficient
% ENTER CODE HERE %
cf(LCV) = ...
end
% Save theta, cf data to file
ascii_out = [x_plot theta cf];
save 'output.txt' -ASCII ascii_out

Accepted Answer

John D'Errico
John D'Errico on 26 Mar 2023
You write:
tau = (mu/(2*delta_y))*(4*un,2-un,3)
But what des that mean to you? Is the fragment
(4*un,2-un,3)
intended to be a vector of length 3? Then you need to use square brackets to create a vector. So you would write:
tau = (mu/(2*delta_y))*[4*un,2-un,3];

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