def test_detection_of_missing_arrays_for_integrator(self):
# Given.
x = np.asarray([1.0])
u = np.asarray([0.0])
h = np.ones_like(x)
pa = get_particle_array(name='fluid', x=x, u=u, h=h, m=h)
arrays = [pa]
# When
integrator = LeapFrogIntegrator(fluid=LeapFrogStep())
equations = [SHM(dest="fluid", sources=None)]
kernel = CubicSpline(dim=1)
a_eval = AccelerationEval(particle_arrays=arrays,
equations=equations,
kernel=kernel)
comp = SPHCompiler(a_eval, integrator=integrator)
# Then
self.assertRaises(RuntimeError, comp.compile)
def test_leapfrog(self):
# Given.
integrator = LeapFrogIntegrator(fluid=LeapFrogStep())
equations = [SHM(dest="fluid", sources=None)]
self._setup_integrator(equations=equations, integrator=integrator)
tf = np.pi
dt = 0.02 * tf
# When
energy = []
def callback(t):
x, u = self.pa.x[0], self.pa.u[0]
energy.append(0.5 * (x * x + u * u))
callback(0.0)
self._integrate(integrator, dt, tf, callback)
# Then
energy = np.asarray(energy)
self.assertAlmostEqual(np.max(np.abs(energy - 0.5)), 0.0, places=3)
def test_leapfrog_is_second_order(self):
# Given.
integrator = LeapFrogIntegrator(fluid=LeapFrogStep())
equations = [SHM(dest="fluid", sources=None)]
self._setup_integrator(equations=equations, integrator=integrator)
# Take a dt, find the error, halve dt, and see that error is drops as
# desired.
# When
tf = np.pi
dt = 0.02 * tf
energy = []
def callback(t):
x, u = self.pa.x[0], self.pa.u[0]
energy.append(0.5 * (x * x + u * u))
callback(0.0)
self._integrate(integrator, dt, tf, callback)
energy = np.asarray(energy)
err1 = np.max(np.abs(energy - 0.5))
# When
self.pa.x[0] = 1.0
self.pa.u[0] = 0.0
energy = []
dt *= 0.5
callback(0.0)
self._integrate(integrator, dt, tf, callback)
energy = np.asarray(energy)
err2 = np.max(np.abs(energy - 0.5))
# Then
self.assertTrue(err2 < err1)
self.assertAlmostEqual(err1 / err2, 4.0, places=2)