Simulate the laws of fluid mechanic

Sure, here’s an example program using the PySPH library to simulate fluid mechanics. In this example, we simulate the flow of an incompressible fluid around a cylinder using the Navier-Stokes equations.

pythonCopy codeimport numpy as np
from pysph.base.utils import get_particle_array
from pysph.solver.application import Application
from pysph.sph.scheme import WCSPHScheme
from pysph.sph.integrator_step import WCSPHStep
from pysph.sph.equation import Group
from pysph.sph.kernel import CubicSpline

# Set up the simulation parameters
fluid_rho = 1000.0  # Density of the fluid
fluid_visc = 0.001  # Viscosity of the fluid
dx = 0.1  # Particle spacing
hdx = 1.5  # Ratio of smoothing length to particle spacing
L = 4.0  # Length of the domain
H = 1.0  # Height of the domain
cylinder_radius = 0.2  # Radius of the cylinder
Umax = 1.0  # Maximum velocity of the fluid

# Set up the particle arrays for the fluid and the cylinder
x, y = np.mgrid[dx/2:L:dx, dx/2:H:dx]
x = x.ravel()
y = y.ravel()
fluid = get_particle_array(x=x, y=y, name='fluid')
fluid.rho[:] = fluid_rho
fluid.m[:] = fluid_rho * dx * dx
fluid.h[:] = hdx * dx
fluid.u[:] = Umax * (1 - (2*cylinder_radius*y*y) / (H*H))
fluid.v[:] = 0.0
cylinder = get_particle_array(name='cylinder')
cylinder.add_property('radius')
cylinder.x[:] = L/4
cylinder.y[:] = H/2
cylinder.radius[:] = cylinder_radius

# Set up the equations for the simulation
kernel = CubicSpline(dim=2)
fluid_equations = [
    Group(
        equations=[
            WCSPHStep(),
            'fluid_accel',
            'fluid_pressure',
            'fluid_viscosity'
        ],
        real=False
    ),
    Group(
        equations=[
            'density',
            'sph_correction',
        ],
        real=True
    ),
    Group(
        equations=[
            'momentum',
        ],
        real=True
    ),
]
cylinder_equations = [
    Group(
        equations=[
            'rigid_body_motion',
        ],
        real=False
    ),
]

# Set up the application and run the simulation
class CylinderInFluid(Application):
    def initialize(self):
        self.scheme = WCSPHScheme(
            fluids=['fluid'], solids=['cylinder'], dim=2, kernel=kernel
        )

    def create_particles(self):
        return [fluid, cylinder]

    def create_equations(self):
        equations = fluid_equations + cylinder_equations
        return equations

app = CylinderInFluid()
app.run()

This program sets up the particle arrays for the fluid and the cylinder using the get_particle_array function from PySPH. We then set up the equations for the simulation, including the Navier-Stokes equations for the fluid and the rigid body motion equations for the cylinder. Finally, we use the WCSPHScheme class from PySPH to integrate the equations over time and obtain the simulation results.

This example simulates the flow of an incompressible fluid around a cylinder using the weakly compressible smoothed particle hydrodynamics (WCSPH) method. The fluid is initialized with a density and viscosity, and a velocity profile that