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Bidimensional Particle Sedimentation (Grid Packing)

This example illustrates the sedimentation of solid particles in a viscous fluid under gravity in two dimensions.

Keywords

FEM, DEM, Generation

Description

The test demonstrates: - How to generate a rectangular 2D mesh with physical boundary tags. - How to define a gravity-driven sedimentation of dense particles. - How to couple the particle solver (scontact) and the fluid solver in MigFlow. - How to export derived fields (pressure, velocity, porosity) for post-processing.

import os, sys, shutil
import numpy as np
import gmsh
from migflow import fluid, scontact, time_integration

Output Directory

The output directory is (re)created

outputdir = "output" if len(sys.argv) < 2 else sys.argv[1]
shutil.rmtree(outputdir, ignore_errors=True)
os.makedirs(outputdir)

Geometrical parameters and mesh generation

A rectangular 2D mesh is generated using Gmsh with named boundaries.

height = 0.6  # domain height [m]
width = 0.4  # domain width [m]
mesh_size = 0.01  # mesh size [m]
h = 1.5e-1  # particle bed height [m]
w = 4e-1  # particle bed width [m]
origin = [-width / 2, -height / 2]  # lower-left corner of the domain
eps = 1e-8  # numerical tolerance


# Function to generate the mesh
def gen_mesh(width, height, mesh_size, origin=np.array([0, 0])):
    """Generate a rectangular 2D mesh with named boundaries."""
    origin = np.asarray(origin)
    gmsh.model.add("box")
    gmsh.model.occ.add_rectangle(origin[0], origin[1], 0, width, height)
    gmsh.model.occ.synchronize()

    def get_line(x0, x1, eps=1e-6):
        r = gmsh.model.get_entities_in_bounding_box(
            x0[0] - eps, x0[1] - eps, -eps, x1[0] + eps, x1[1] + eps, eps, 1
        )
        return [tag for dim, tag in r]

    h, w = height, width
    gmsh.model.add_physical_group(
        1, get_line(origin + [0, 0], origin + [w, 0]), name="Bottom"
    )
    gmsh.model.add_physical_group(
        1, get_line(origin + [0, h], origin + [w, h]), name="Top"
    )
    gmsh.model.add_physical_group(
        1, get_line(origin + [0, 0], origin + [0, h]), name="Left"
    )
    gmsh.model.add_physical_group(
        1, get_line(origin + [w, 0], origin + [w, h]), name="Right"
    )
    gmsh.model.add_physical_group(2, [1], name="domain")
    gmsh.model.mesh.set_size_callback(lambda dim, tag, x, y, z, lc: mesh_size)
    gmsh.model.mesh.generate(2)


gen_mesh(width, height, mesh_size, origin)

Physical Parameters

g = np.array([0, -9.81])  # gravity [m/s²]
r = 1.5e-3  # particle radius [m]
rhop = 1500  # particle density [kg/m³]
rho = 1000  # fluid density [kg/m³]
nu = 1e-6  # kinematic viscosity [m²/s]
mu = nu * rho  # dynamic viscosity [Pa·s]

Particle Problem Initialization

Particles are placed in a rectangular patch at the top of the domain.

p = scontact.ParticleProblem(2)
p.set_fixed_contact_geometry(0)
p.load_msh_boundaries(None, ["Top", "Left", "Right", "Bottom"])

Grid Generation

Define particle positions in a grid with small random perturbations.

lx = w - 2 * r - eps
ly = h
y0 = height / 2 - r - eps
step = 2 * r + eps
x = np.arange(-lx / 2, lx / 2 - step, step) + step / 2
n = x.shape[0]
x_off = lx - n * step
x += x_off / 2
y = np.arange(y0, y0 - h, -step)
x, y = np.meshgrid(x, y)
for xi, yi in zip(x.flat, y.flat):
    p.add_particle((xi, yi), r, r**2 * np.pi * rhop)

Fluid Problem Initialization

The fluid solver is initialized using the generated mesh. All walls are no-slip.

f = fluid.FluidProblem(2, g, mu, rho)
f.load_msh(None)
f.set_wall_boundary("Bottom")
f.set_wall_boundary("Left")
f.set_wall_boundary("Right")
f.set_wall_boundary("Top")
f.set_mean_pressure(0)


def get_fields(fluid):
    """Return derived fields for output."""
    y = fluid.coordinates_fields()[fluid.pressure_index()][:, 1]
    y = y.reshape(-1, 1)
    p1_element = fluid.get_p1_element()
    return {
        "pressure": (fluid.pressure(), p1_element),
        "velocity": (fluid.velocity(), p1_element),
        "porosity": (fluid.porosity(), p1_element),
        "u_solid": (fluid.u_solid(), p1_element),
        "dynamic_pressure": (fluid.pressure() - rho * g[1] * y, p1_element),
    }

Simulation Parameters

outf = 1  # number of iterations between outputs
dt = 1e-2  # time step [s]
tEnd = 2  # final time [s]
t = 0
i = 0

Computational Loop

mass = np.pi * p.r() ** 2 * rhop
while t < tEnd:
    print(f"{i:4d}, {t:.6g}/{tEnd:.6g}")
    # Coupling: update particle data in the fluid solver
    f.set_particles(
        p.delassus(),
        p.volume(),
        p.position(),
        p.velocity(),
        p.omega(),
        p.contact_forces(),
    )
    # Write outputs
    if i % outf == 0:
        f.write_mig(outputdir, t, get_fields(f))
        p.write_mig(outputdir, t)

    # Fluid and particle update
    f.implicit_euler(dt)
    fext = g * mass + f.compute_node_force()
    time_integration._advance_particles(p, fext, dt, 1, 1e-4 * r)

    # Time stepping
    t += dt
    i += 1

Plot

python3 -m migflow.plot.migplot output --actors fluid particles --fluid-field velocity