Use navier stokes equation or Darcy equation in the form of PDE and code it in matlab to solve a case study like water movement or oil movement in reservoirs.

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clear all;
w = 1e+6;
beta = 0.5;
L = 2;
c = 1/(beta);
dt = 1e-8;
dx = 1e-2;
p = c*dt/dx;
Nt = 1e+3;
Nx = L/dx;
x = 0:dx:(Nx-1)*dx;
t = 0:dt:(Nt-1)*dt;
v1(1,:) = 10*cos(w*t);

for i = 1:Nx-1
    for j = 1:Nt-1
       if (j>=2 && i>=2)
            v1(i+1,j) = (1/(p*p))*(v1(i,j+1)-p*p*v1(i-1,j)-2*(1-(p*p))*v1(i,j)+v1(i,j-1...

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