Shallow Water Tutorial 2d with JAX (Simple)

Contents

Shallow Water Tutorial 2d with JAX (Simple)#

The following verification is based on the paper: 

```
 @article{Delestre_2013, 
 title={SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies}, 
 volume={72}, 
 ISSN={0271-2091, 1097-0363}, DOI={10.1002/fld.3741}, 
 note={arXiv:1110.0288 [physics]}, 
 number={3}, 
 journal={International Journal for Numerical Methods in Fluids}, 
 author={Delestre, Olivier and Lucas, Carine and Ksinant, Pierre-Antoine and Darboux, Frédéric and Laguerre, Christian and Vo, Thi Ngoc Tuoi and James, Francois and Cordier, Stephane}, 
 year={2013}, 
 month=may, 
 pages={269–300} 
}
```

Imports#

# | code-fold: true
# | code-summary: "Load packages"
# | output: false

import sys
import os
import numpy as np
import pytest
from sympy import Matrix

from zoomy_jax.fvm.solver_jax import HyperbolicSolver, Settings
from zoomy_core.fvm.solver_numpy import HyperbolicSolver as NumpyHyperbolicSolver
from zoomy_core.model.basemodel import Model
from attr import field, define
import zoomy_core.model.initial_conditions as IC
import zoomy_core.model.boundary_conditions as BC
import zoomy_core.misc.io as io
from zoomy_jax.mesh.mesh import compute_derivatives
from zoomy_core.misc.misc import Zstruct, ZArray
from zoomy_tests.swashes import plots_paper
from zoomy_core.fvm import timestepping

import zoomy_core.misc.misc as misc
from zoomy_core.mesh import BaseMesh
import zoomy_core.postprocessing.postprocessing as postprocessing

@define(frozen=True, slots=True, kw_only=True)
class SWE(Model):
    dimension: int = 1
    variables: Zstruct = field(init=False)
    aux_variables: Zstruct = field(default=1)
    _default_parameters: dict = field(
        init=False, factory=lambda: {"g": 9.81, "ex": 0.0, "ey": 0.0, "ez": 1.0}
    )
    
    def __attrs_post_init__(self):
        object.__setattr__(self, "variables", self.dimension + 1)
        super().__attrs_post_init__()

    def project_2d_to_3d(self):
        out = ZArray.zeros(6)
        dim = self.dimension
        z = self.position[2]
        b = 0
        h = self.variables[0]
        U = [hu / h for hu in self.variables[1 : 1 + dim]]
        rho_w = 1000.0
        g = 9.81
        out[0] = b
        out[1] = h
        out[2] = U[0]
        out[3] = 0 if dim == 1 else U[1]
        out[4] = 0
        out[5] = rho_w * g * h * (1 - z)
        return out

    def flux(self):
        dim = self.dimension
        h = self.variables[0]
        U = Matrix([hu / h for hu in self.variables[1 : 1 + dim]])
        g = self.parameters.g
        I = Matrix.eye(dim)
        F = Matrix.zeros(self.variables.length(), dim)
        F[0, :] = h * U.T
        F[1:, :] = h * U * U.T + g / 2 * h**2 * I

        return F

bcs = BC.BoundaryConditions(
    [
        BC.Extrapolation(tag="wall"),
        BC.Extrapolation(tag="inflow"),
        BC.Extrapolation(tag="outflow"),
    ]
)

def custom_ic(x):
    Q = np.zeros(3, dtype=float)
    Q[0] = np.where(x[0] < 5.0, 0.005, 0.001)
    return Q


ic = IC.UserFunction(custom_ic)

model = SWE(
    dimension=2,
    boundary_conditions=bcs,
    initial_conditions=ic,
)

main_dir = misc.get_main_directory()

mesh = petscMesh.Mesh.from_gmsh(
    os.path.join(main_dir, "meshes/channel_quad_2d/mesh.msh")
)

class SWESolver(NumpyHyperbolicSolver):
    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[2]/Q[0], mesh, derivatives_multi_index=[[0, 1]])[:,0]
        # Qaux = Qaux.at[0].set(dudx)
        # Qaux = Qaux.at[1].set(dvdy)
        return Qaux
    
settings = Settings(name="ShallowWater", output=Zstruct(directory="outputs/shallow_water_2d", filename="swe", clean_directory=True))
solver = SWESolver(time_end=6, settings=settings, compute_dt=timestepping.adaptive(CFL=0.45),)
Qnew, Qaux = solver.solve(mesh, model)



2025-11-20 15:37:08.637 | WARNING  | zoomy_core.misc.misc:__init__:197 - No 'snapshots' attribute found in output Zstruct. Default: 2
2025-11-20 15:37:10.157 | INFO     | zoomy_core.fvm.solver_numpy:run:285 - iteration: 10, time: 1.123197, dt: 0.104860, next write at time: 6.000000
2025-11-20 15:37:11.411 | INFO     | zoomy_core.fvm.solver_numpy:run:285 - iteration: 20, time: 2.146722, dt: 0.101170, next write at time: 6.000000
2025-11-20 15:37:12.496 | INFO     | zoomy_core.fvm.solver_numpy:run:285 - iteration: 30, time: 3.151076, dt: 0.100059, next write at time: 6.000000
2025-11-20 15:37:13.611 | INFO     | zoomy_core.fvm.solver_numpy:run:285 - iteration: 40, time: 4.148888, dt: 0.099623, next write at time: 6.000000
2025-11-20 15:37:14.761 | INFO     | zoomy_core.fvm.solver_numpy:run:285 - iteration: 50, time: 5.143900, dt: 0.099419, next write at time: 6.000000
2025-11-20 15:37:15.662 | INFO     | zoomy_core.fvm.solver_numpy:solve:295 - Finished simulation with in 6.808 seconds

io.generate_vtk(os.path.join(settings.output.directory, f"{settings.output.filename}.h5"))
postprocessing.vtk_project_2d_to_3d(model, settings, filename='out_3d')

2025-11-20 15:37:18.638 | INFO     | zoomy_core.postprocessing.postprocessing:vtk_project_2d_to_3d:71 - Converted snapshot 0/2
2025-11-20 15:37:18.656 | INFO     | zoomy_core.postprocessing.postprocessing:vtk_project_2d_to_3d:71 - Converted snapshot 1/2
2025-11-20 15:37:18.804 | INFO     | zoomy_core.postprocessing.postprocessing:vtk_project_2d_to_3d:74 - Output is written to: /workspace/outputs/shallow_water_2d/out_3d.h5/out_3d.*.vtk

fig = plots_paper.plot_swe(os.path.join(settings.output.directory, settings.output.filename + ".h5"))

{'length': 10.0, 'width': None, 'dx': 0.2, 'dy': None, 'ncellx': 50.0, 'ncelly': None}
../../../_images/8a37ef03e06d897d1206ff35b83888184135677d3d77094f14d11cf125b6ff16.png 
@pytest.mark.nbworking
def test_working():
    assert True
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