Example of the BoreFlow package

Example calculation of a predefined flow on a horizontal surface and a steep slope.

import numpy as np
import matplotlib.pyplot as plt

from boreflow import BCArray, Geometry, Simulation, Flux, Limiter, TimeIntegration

# 1) Create geometry
x = np.array([0, 2, 11])  # X-coordinate x[i]
z = np.array([3, 3, 0])  # Elevation z[i] at x[i]
n = np.array([0.0175, 0.0175])  # Manning roughness (n) between x[i] and x[i+1]
geometry = Geometry(x, z, n)

# Plot the geometry
plt.figure()
plt.plot(x, z, color="black", label="Geometry")
plt.plot([x[0]], [z[0]], "o", color="red", label="Inflow")
plt.plot([x[-1]], [z[-1]], "o", color="blue", label="Free outflow")
plt.legend()
plt.xlabel("x-coordinate [m]")
plt.ylabel("z-coordinate [m]")
plt.axis("equal")
plt.show()

# 2) Create boundary conditions
t = np.array([0, 1, 4])
h = np.array([0.5, 0.8, 0])
u = np.array([1.0, 2.0, 0])
bc = BCArray(t, h, u)

# 3) Initialize simulation settings
sim = Simulation(t_end=10.0, cfl=0.2, max_dt=0.01, nx=110)

# 4) Run the simulation
results = sim.run(geometry, bc, Limiter.minmod, Flux.HLL, TimeIntegration.EF)

Simulating:   0%|          | 0.00/10.00 sSimulating:   6%|▌         | 0.55/10.00 sSimulating:  11%|█         | 1.10/10.00 sSimulating:  15%|█▍        | 1.49/10.00 sSimulating:  18%|█▊        | 1.78/10.00 sSimulating:  20%|██        | 2.01/10.00 sSimulating:  22%|██▏       | 2.19/10.00 sSimulating:  23%|██▎       | 2.33/10.00 sSimulating:  25%|██▍       | 2.45/10.00 sSimulating:  26%|██▌       | 2.56/10.00 sSimulating:  27%|██▋       | 2.65/10.00 sSimulating:  27%|██▋       | 2.74/10.00 sSimulating:  28%|██▊       | 2.82/10.00 sSimulating:  29%|██▉       | 2.89/10.00 sSimulating:  30%|██▉       | 2.96/10.00 sSimulating:  30%|███       | 3.03/10.00 sSimulating:  31%|███       | 3.10/10.00 sSimulating:  32%|███▏      | 3.17/10.00 sSimulating:  32%|███▏      | 3.24/10.00 sSimulating:  33%|███▎      | 3.31/10.00 sSimulating:  34%|███▍      | 3.38/10.00 sSimulating:  35%|███▍      | 3.45/10.00 sSimulating:  35%|███▌      | 3.52/10.00 sSimulating:  36%|███▌      | 3.59/10.00 sSimulating:  37%|███▋      | 3.66/10.00 sSimulating:  37%|███▋      | 3.73/10.00 sSimulating:  38%|███▊      | 3.81/10.00 sSimulating:  39%|███▉      | 3.88/10.00 sSimulating:  40%|███▉      | 3.95/10.00 sSimulating:  40%|████      | 4.03/10.00 sSimulating:  41%|████      | 4.11/10.00 sSimulating:  42%|████▏     | 4.18/10.00 sSimulating:  43%|████▎     | 4.26/10.00 sSimulating:  43%|████▎     | 4.34/10.00 sSimulating:  44%|████▍     | 4.42/10.00 sSimulating:  45%|████▌     | 4.50/10.00 sSimulating:  46%|████▌     | 4.58/10.00 sSimulating:  47%|████▋     | 4.67/10.00 sSimulating:  48%|████▊     | 4.75/10.00 sSimulating:  48%|████▊     | 4.84/10.00 sSimulating:  49%|████▉     | 4.93/10.00 sSimulating:  50%|█████     | 5.02/10.00 sSimulating:  51%|█████     | 5.11/10.00 sSimulating:  52%|█████▏    | 5.21/10.00 sSimulating:  53%|█████▎    | 5.30/10.00 sSimulating:  54%|█████▍    | 5.40/10.00 sSimulating:  55%|█████▌    | 5.51/10.00 sSimulating:  56%|█████▌    | 5.61/10.00 sSimulating:  57%|█████▋    | 5.72/10.00 sSimulating:  58%|█████▊    | 5.84/10.00 sSimulating:  60%|█████▉    | 5.95/10.00 sSimulating:  61%|██████    | 6.08/10.00 sSimulating:  62%|██████▏   | 6.20/10.00 sSimulating:  63%|██████▎   | 6.34/10.00 sSimulating:  65%|██████▍   | 6.48/10.00 sSimulating:  66%|██████▋   | 6.63/10.00 sSimulating:  68%|██████▊   | 6.78/10.00 sSimulating:  69%|██████▉   | 6.94/10.00 sSimulating:  71%|███████   | 7.11/10.00 sSimulating:  73%|███████▎  | 7.29/10.00 sSimulating:  75%|███████▍  | 7.48/10.00 sSimulating:  77%|███████▋  | 7.68/10.00 sSimulating:  79%|███████▉  | 7.88/10.00 sSimulating:  81%|████████  | 8.11/10.00 sSimulating:  83%|████████▎ | 8.34/10.00 sSimulating:  86%|████████▌ | 8.58/10.00 sSimulating:  88%|████████▊ | 8.83/10.00 sSimulating:  91%|█████████ | 9.08/10.00 sSimulating:  93%|█████████▎| 9.33/10.00 sSimulating:  96%|█████████▌| 9.58/10.00 sSimulating:  98%|█████████▊| 9.83/10.00 sSimulating: 100%|██████████| 10.00/10.00 s

Simulation done in 8.20 sec

# Plot peak flow velocity and peak flow thickness
fig, (ax0, ax1, ax2) = plt.subplots(1, 3, figsize=[8, 3.5])

# Mark the transition between the horizontal surface and the sloped surface (x = 2m / s = 2m)
[ax.axvline(2.0, color="grey", ls=":") for ax in [ax0, ax1, ax2]]

# Get and plot peak flow characteristics
h, u, q = results.get_peak_flow()
ax0.plot(results.s, h, color="black")
ax1.plot(results.s, u, color="black")
ax2.plot(results.s, q, color="black")

# Plot layout
[ax.set_xlabel("Distance along geometry (s-coordinate) [m]") for ax in [ax0, ax1, ax2]]
ax0.set_ylabel("Peak flow thickness [m]")
ax1.set_ylabel("Peak depth-avg flow velocity [m/s]")
ax2.set_ylabel("Peak flow discharge [m2/s]")
[ax.set_xlim(0, np.max(results.s)) for ax in [ax0, ax1, ax2]]
[ax.set_ylim(0, None) for ax in [ax0, ax1, ax2]]
fig.suptitle("Peak Flow Characteristics along Geometry")
fig.tight_layout()
plt.show()

# Plot
fig, (ax0, ax1) = plt.subplots(1, 2, figsize=[8, 4])

# Get and plot the flow at s=5m
res_t, res_h, res_u = results.get_st(s=5.0)
ax0.plot(res_t, res_h, color="black")
ax1.plot(res_t, res_u, color="black")

# Plot layout
[ax.set_xlabel("Time [s]") for ax in [ax0, ax1]]
ax0.set_ylabel("Flow thickness [m]")
ax1.set_ylabel("Depth-avg flow velocity [m/s]")
[ax.set_xlim(0, np.max(res_t)) for ax in [ax0, ax1]]
[ax.set_ylim(0, None) for ax in [ax0, ax1]]
fig.suptitle("Temporal Evolution of Flow at s = 5m")
fig.tight_layout()
plt.show()