Groundwater Flow Model Characteristics
- 1-D
- 100 meter length
- 1 meter unit width
- 1 meter unit depth
- 0.1 day time step
- Plot distribution at t=0, 3, 20, and 100 days
Aquifer Characteristics
- Steady State
- Confined
- Homogenous
- Isotropic
- Hydraulic Conductivity of 10 meters per day
- Specific Storage of 1 per meter
Pumping Well Characteristics
- Located at center node (50 meters from either side)
- Pumping Rate of 1 m3/day (constant beginning at t=0)
Boundary Conditions
- Constant head of 8 at left boundary
- Constant head of 10 at right boundary
Declare the model characteristics
k = 10;
Ss = 1;
Q = 1;
dx = 1;
dt = 0.1;
duration = 100;
h = zeros(100, 1001);
h(:, 1) = linspace(8, 10, 100);
h(1, :) = 8;
h(100, :) = 10;
n = 98;
h2 = h(2:100, 1);
a = -1;
b = 2 + Ss / k * dx^2 / dt;
c = -1;
beta(1) = b;
for j = 2:n
alpha(j) = a / beta(j - 1);
beta(j) = b - a * alpha(j);
end
for t = 2:duration / dt + 1
f = h2;
f(1) = f(1) + 8;
f(n) = f(n) + 10;
f(50) = f(50) - 0.1;
y(1, 1) = f(1);
for j = 2:n;
y(j, 1) = f(j) - alpha(j) * y(j - 1);
end
h2(n, 1) = y(n) / beta(n);
for i = n - 1:-1:1
h2(i, 1) = (y(i) -c * h2(i + 1, 1)) / beta(i);
end
h(2:100, t) = h2;
end
Plot the results
plot(1:100, h(:, 1)); hold on;
plot(1:100, h(:, 31)); hold on;
plot(1:100, h(:, 201)); hold on;
plot(1:100, h(:, 1001));
legend('t=0', 't=3', 't=20', 't=100')
xlabel('Length(m)');
ylabel('Head (m)');
title('Matlab Head Distribution')
