Author

Ingo Steldermann

Published

July 10, 2025

Shallow Moment Tutorial (Simple)

Imports

Load packages 
import os
import numpy as np
import jax
from jax import numpy as jnp
import pytest
from types import SimpleNamespace
from sympy import cos, pi, Piecewise

from fvm.solver_jax import HyperbolicSolver, Settings
from fvm.ode import RK1
import fvm.reconstruction as recon
import fvm.timestepping as timestepping
import fvm.flux as flux
import fvm.nonconservative_flux as nc_flux
from zoomy_core.model.boundary_conditions import BoundaryCondition
from zoomy_core.model.models.basisfunctions import Basisfunction, Legendre_shifted
from zoomy_core.model.models.basismatrices import Basismatrices
from misc.misc import Zstruct

from zoomy_core.model.models.shallow_moments import ShallowMoments2d
import zoomy_core.model.initial_conditions as IC
import zoomy_core.model.boundary_conditions as BC
import misc.io as io
from mesh.mesh import compute_derivatives
from zoomy_tests.swashes import plots_paper
import postprocessing.visualization as visu


import mesh.mesh as petscMesh
import postprocessing.postprocessing as postprocessing
from mesh.mesh import convert_mesh_to_jax
import argparse

Model

level = 0
offset = 1+level
n_fields = 3 + 2 * level
settings = Settings(
    name="SME",
    output=Zstruct(
        directory=f"outputs/junction_{level}", filename="SME", output_snapshots=30
    ),
)
2025-08-30 07:18:44.091 | WARNING  | library.misc.misc:__init__:146 - No 'clean_directory' attribute found in output Zstruct. Default: False

inflow_dict = { 
    0: lambda t, x, dx, q, qaux, p, n: Piecewise((0.1, t < 0.2),(q[0], True)),
    1: lambda t, x, dx, q, qaux, p, n: Piecewise((-0.3, t < 0.2),(-q[1], True)),
                }
inflow_dict.update({
    1+i: lambda t, x, dx, q, qaux, p, n: 0 for i in range(level)
})
inflow_dict.update({
    1+offset+i: lambda t, x, dx, q, qaux, p, n: 0 for i in range(level+1)
})

bcs = BC.BoundaryConditions(
    [
        BC.Lambda(tag="inflow", prescribe_fields=inflow_dict),
        BC.Wall(tag="wall"),
    ]
)

def custom_ic(x):
    Q = np.zeros(3 + 2 * level, dtype=float)
    Q[0] = 0.01
    return Q

ic = IC.UserFunction(custom_ic)

model = ShallowMoments2d(
    level=level,
    boundary_conditions=bcs,
    initial_conditions=ic,
)

main_dir = os.getenv("ZOOMY_DIR")
mesh = petscMesh.Mesh.from_gmsh(
    os.path.join(main_dir, "meshes/channel_junction/mesh_2d_coarse.msh")
    # os.path.join(main_dir, "meshes/channel_junction/mesh_2d_fine.msh")
)

mesh = convert_mesh_to_jax(mesh)
class SMESolver(HyperbolicSolver):
    def update_qaux(self, Q, Qaux, Qold, Qauxold, mesh, model, parameters, time, dt):
        dudx = compute_derivatives(Q[1]/Q[0], mesh, derivatives_multi_index=[[0, 0]])[:,0]
        dvdy = compute_derivatives(Q[1+offset]/Q[0], mesh, derivatives_multi_index=[[0, 1]])[:,0]
        Qaux = Qaux.at[0].set(dudx)
        Qaux = Qaux.at[1].set(dvdy)
        return Qaux
solver = SMESolver(settings=settings)

Solve

Qnew, Qaux = solver.solve(mesh, model)
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2025-08-30 07:19:02.045 | INFO     | library.fvm.solver_jax:log_callback_execution_time:56 - Finished simulation with in 9.556 seconds

Visualization

io.generate_vtk(os.path.join(settings.output.directory, f"{settings.output.filename}.h5"))
# postprocessing.vtk_project_2d_to_3d(model, settings, Nz=20, filename='out_3d')
# visu.pyvista_3d(settings.output.directory, scale=1.0)