Flow on a hillslope

This tutorial demonstrates how to use the pipedream solver to simulate the flow of water on a simple hillslope.

Import modules

import numpy as np
import pandas as pd
from pipedream_solver.hydraulics import SuperLink

Load model data

Model structure can be saved to or loaded from CSV files. In this case, our model consists of a set of superjunctions and a set of superlinks.

input_path = '../data/hillslope'
superjunctions = pd.read_csv(f'{input_path}/hillslope_superjunctions.csv')
superlinks = pd.read_csv(f'{input_path}/hillslope_superlinks.csv')

Superjunctions

Superjunctions are basic finite volumes, and may represent manholes, retention ponds, or other bodies of water.

superjunctions

	name	id	z_inv	h_0	bc	storage	a	b	c	max_depth	map_x	map_y
0	0	0	1	0.00001	False	functional	0.0	0.0	200.0	inf	0	0
1	1	1	0	0.00001	False	functional	0.0	0.0	1000.0	inf	1	1

Superlinks

Superlinks are sections of channel or conduit that connect superjunctions together. Each superlink consists of a number of internal junctions and nodes connected in a linear fashion. In this case, we have a single superlink that connects the uphill superjunction to the downhill superjunction.

superlinks

	name	id	sj_0	sj_1	in_offset	out_offset	dx	n	shape	g1	g2	g3	g4	Q_0	h_0	ctrl	A_s	A_c	C
0	0	0	0	1	0.0	0.0	1000	0.035	rect_open	10	5	0	0	0	0.00001	False	100	0	0

Internal links and junctions can be specified explicitly, or generated automatically inside each superlink. In this case, we will use 24 automatically-generated internal links.

internal_links = 24

Instantiate model

The hydraulic model is instantiated with the SuperLink class.

model = SuperLink(superlinks, superjunctions, 
                  internal_links=internal_links)

Next, we specify the model parameters, including the default time step dt, the inflow into each superjunction Q_in, and the inflow into each internal junction Q_0Ik.

dt = 10                            # Model time step (s)
Q_in = 1e-3 * np.ones(model.M)     # Flow into each internal junction (cms)
Q_0Ik = 1e-3 * np.ones(model.NIk)  # Flow into each internal junction (cms)

Note that model.M is the number of superjunctions, and model.NIk is the number of internal junctions.

We can visualize the model with plot_profile. Note that the hillslope at the start of the model run is dry.

# Plot profile from superjunctions 0 to 1 (uphill to downhill)
_ = model.plot_profile([0, 1], width=100)

Run model

Apply rain to hillslope for 4 hours

Applying inflow to each superjunction and internal link causes water to flow down the hill.

# For each timestep...
for _ in range(4 * 360):
    # Advance model forward in time
    model.step(dt=dt, Q_in=Q_in, Q_0Ik=Q_0Ik)

_ = model.plot_profile([0, 1], width=100)

Progress forward in time for 3 hours with no rain

Ceasing the flow input and advancing the model in time causes the water to settle at the bottom of the hill.

for _ in range(3 * 360):
    model.step(dt=dt)

_ = model.plot_profile([0, 1], width=100)