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2D lid-driven cavity flow

This example simulates a 2D lid-driven cavity flow using the Finite Element Method (FEM) with a P1-P1 representation.

Keywords

FEM, lid driven cavity, 2D, fluid

Description

The test demonstrates: - How to perform a FEM simulation in a fixed domain

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

Output Directory

Create a clean output directory for simulation results.

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

l_box = 1.0
h_box = 1.0

Mesh parameters

mesh_size = l_box / 80


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(l_box, h_box, mesh_size)

Physical Parameters

g = np.array([0.0, 0.0])
rho = 1000
mu = 1e-3
Re = 1000
v_top = Re * mu / (rho * l_box)

Time parameters

cfl = 1
U = v_top
U_init = v_top
dt = mesh_size / U * cfl
t = 0
tEnd = 25000.0

Fluid problem

f = fluid.FluidProblem(2, g, mu, rho)
f.load_msh(None)
f.set_wall_boundary("bottom", velocity=[0, 0])
f.set_wall_boundary("right", velocity=[0, 0])
f.set_wall_boundary("top", velocity=[v_top, 0])
f.set_wall_boundary("left", velocity=[0, 0])
f.set_strong_boundary("top", velocity=[v_top, 0])
f.set_strong_boundary("bottom", velocity=[0, 0])
f.set_strong_boundary("left", velocity=[0, 0])
f.set_strong_boundary("right", velocity=[0, 0])

Simulation Loop

Time integration loop.

i = 0
outf = 25
while t < tEnd:
    print(f"{i:4d}, {t:.6g}/{tEnd:.6g}, {dt:.6g}")
    if i % outf == 0:  # or t > 0.3:
        f.write_mig(outputdir, t)
    f.implicit_euler(dt)
    t += dt
    i += 1

Plot

python3 -m migflow.plot.migplot output --actors fluid --fluid-field velocity --fluid-vmin 0 --fluid-vmax 0.001