3D Darcy flow

Here we illustrate Darcy flow in a heterogeneous 3D body. We use the general pygimli.solver.solveFiniteElements() to solve Darcy’s law:

\[\nabla \cdot(K \nabla p)=0\]

The sought hydraulic velocity distribution can then be calculated as the gradient field of \(\mathbf{v}=-\nabla p\).

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<pyvista.plotting.plotting.Plotter object at 0x7ff376ed98b0>

import numpy as np

import pygimli as pg
import pygimli.meshtools as mt
from pygimli.viewer.pv import drawStreamLines, drawSlice

plc = mt.createCube(size=[40, 20, 15], marker=1, boundaryMarker=0)
cube = mt.createCube(size=[15, 15, 8], marker=2, boundaryMarker=0)
geom = plc + cube

mesh = mt.createMesh(geom, area=4)

for bound in mesh.boundaries():
    x = bound.center().x()
    if x == mesh.xmin():
        bound.setMarker(1)
    elif x == mesh.xmax():
        bound.setMarker(2)

kMap = {1: 1e-4, 2: 1e-6}
kArray = pg.solver.parseMapToCellArray(list(kMap), mesh) # dict does not work
kArray = np.column_stack([kArray] * 3)

bc = {"Dirichlet": {1: 20.0, 2: 10.0}}


h = pg.solver.solveFiniteElements(mesh, kMap, bc=bc)
vel = -pg.solver.grad(mesh, h) * kArray

pg.show(mesh, h, label="Hydraulic head (m)")

ax, _ = pg.show(mesh, alpha=0.3, hold=True, colorBar=False)
drawStreamLines(ax, mesh, vel, radius=.1, source_radius=10)
drawSlice(ax, mesh, normal=[0,1,0], data=pg.abs(vel), label="Absolute velocity")
# ax.show()