def UpdateFluid(self,
f,
Update_du=True,
CalcPressure=False,
UpdateStress=True,
KeepUpdate=True):
"""Advance the fluid one timestep via a semi-implicit scheme.
f is a force field applied to the fluid at the current time and must be a vector field."""
# Calculate polymeric stress contribution
self.CurrentStress = self.PolymericStress()
f += self.CurrentStress
# Update the fluid
Fluid.UpdateFluid(self, f, Update_du, CalcPressure, KeepUpdate)
# Update the fluid stress
if UpdateStress and KeepUpdate:
self.UpdateS()
# The simulation loop
Time.StartTimer()
while Time.t < Time.T:
Time.PrintStepInfo()
X.CheckForExplosion()
# The FE/BE method
# First calculate the fiber force F (stored in X.F)
X.CalcForceDistribution()
# Spread F to the Eulerian grid, storing the result in the force field u.f
X.ToGrid(u)
# Evolve the fluid forward one time step
u.UpdateFluid(u.f, CalcPressure = True)
# Interpolate the fluid velocity to the fiber (stored in X.U)
X.FromGrid(u)
# Update the fiber position
X.X += dt * X.U
# Update the time
Time.Incr()
Time.PrintTimeInfo()
# Plot the fluid/fiber and save to file
if Time.CurStep % SavePeriod == 0:
m.clf() # Clear the plotter
u.Plot2D(PlotStyle.pressure) # Plot the fluid pressure
from Ellipse import Ellipse
from MatrixUtility import Stack, Unstack
# Simulation parameters
N = 128
RestrictToEulerian = False # If True we restrict the fiber points to Eulerian intersections. When done the matrix should give EXACT results.
# Create the fiber in the shape of an ellipse
X = Ellipse(2 * N, s=10e6, c=[.5, .5], p1=[.8, .5], p2=[.5, .6])
if RestrictToEulerian:
X.X = floor(X.X * N) / N
# Initialize the fluid solver
u = Fluid(dt=1. / N, N=[N, N], dims=[1., 1.])
# Calculate dX/dt (stored in X.U) using a fluid solve
X.CalcForceDistribution()
X.ToGrid(u)
u.UpdateFluid(u.f)
X.FromGrid(u)
# Calculate dX/dt (stored in U) using the fluid matrix
# First construt the fluid matrix
M = X.ConstructFluidMatrix(u)
# Then calculate U = M * F, where F is the fiber force
U = Unstack(dot(M, Stack(X.F)), 2)
# Calculate difference between X.U and U (the induced flow calculated via a fluid solve and via the matrix)
print abs(X.U - U).max() / abs(X.U).max()
