%  Numerical Modelling in Geosciences
%  by Manuele Faccenda, Università di Padova
%
%  Practice 1
%
%  Use of functions for,while,if
%  Produce/plot 1D data

%Better to clear any previous results/data and plot
clear all;
clf;

%% Vertical flow of a fluid in a half-pipe is described by the following function:
%
%   vz(x) = vz0 - x^2 * 50;
%
%  in the range 0 < x < 0.1 m, where vz0 = 1 m/s.

%Min/Max dimensions
Xmin = 0;
Xmax = 1e-1;
%Number of nodes
Xnum = 101;
%Nodes distance
dx = (Xmax-Xmin)/(Xnum-1);
%Initialize x-coordinate array of dimensions (Xnum x 1)
X = zeros(Xnum,1);
%Calculate nodes coordinates
for i = 1 : Xnum
    if i == 1
        X(i) = Xmin;
    else
        X(i)= X(i-1) + dx;
    end
end

%Set v0
vz0 = 1;

%Initialize velocity array of dimensions (xnum x 1)
vz = zeros(Xnum,1);
%"for" loop to calculate v(x)
for i = 1 : Xnum
    vz(i) = vz0 - X(i)^2 * 50;
end
    
%Plot result
figure(1)
plot(X,vz,'r','LineWidth',3)
axis tight

%% Next, assume that the fluid vertical velocity increases every hour by:
%
%   dvz(x) = dvz0 - x * 0.25 (m/s)
%
%  until one of the nodes velocity reaches vz = 2 m/s, after which becomes 
%  steady-state (i.e., time-independent). 
%  Set dvz0 = 0.05 m/s.

%Set dv0,vmax and time variables
dvz0 = 0.05;
vzmax = 2;
time=0;
tstp=3600; %seconds
%Flag
VZ0 = 1;

%Iterate acceleration
while VZ0 > 0
    for i = 1: Xnum
        dvz = dvz0 - X(i) * 0.25;
        vz(i) = vz(i) + dvz;
        if(vz(i) >= vzmax)
            VZ0 = 0;
        end
    end
    %Time increase
    time = time + tstp;
    
    hold on
    plot(X,vz)
    axis tight
    title(['Time: ',num2str(time),' seconds'])
    xlabel('Pipe radius')
    ylabel('Fluid velocity')
    pause(0.1)
end

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%%%                                Homework                                   %%%
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%%%   Please, exercise at home with all the above functions and algorithms.   %%%
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