def testCircleEvolution():
r"""
Evolves an initially circular level set to see if it remains circular.
"""
# create circle
N = 50
t = 0.
X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
r = 0.3
dx = 2.0 / (N - 1)
dy = dx
dt = 0.1
phi = (X)**2 + (Y)**2 - r**2
phi = computeDistanceFunction(phi, dx)
title = "Circle evolution"
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi), title, [0, dx * (N - 4), 0, dx * (N - 4)],
[2, N - 3, 2, N - 3], 0, 0)
plt.show(block=False)
nIt = 200
sL0 = 0.0
marksteinLength = 0.0
u = np.zeros_like(phi)
v = np.zeros_like(phi)
adVel = 0.1 # magnitude of advective velocity
iblims = np.array([2, N - 3, 2, N - 3])
lims = np.array([2, N - 2, 2, N - 2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx * (N - 4), 0, dx * (N - 4)])
# make velocities
hyp = np.sqrt(X[:, :]**2 + Y[:, :]**2)
u[:, :] = adVel * Y[:, :] / hyp[:, :]
v[:, :] = adVel * X[:, :] / hyp[:, :]
# fix signs
u[:N / 2, :] = -1. * np.fabs(u[:N / 2, :])
u[N / 2:, :] = np.fabs(u[N / 2:, :])
v[:, :N / 2] = -1. * np.fabs(v[:, :N / 2])
v[:, N / 2:] = np.fabs(v[:, N / 2:])
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi,
sL0,
marksteinLength,
u,
v,
iblims,
dx=dx,
dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforceOutflowBCs(Fx, lims)
Fy = enforceOutflowBCs(Fy, lims)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo + 1:ihi + 1, jlo:jhi]) / dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo + 1:jhi + 1]) / dy)
t += dt
# enforce outflow boundary conditions
phi = enforceOutflowBCs(phi, lims)
# plotting
dovis(phi, title, gridlims, iblims, n, t, u=u, v=v)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
return
def testPeriodicVortexEvolution():
r"""
Evolves a circle in periodic vortex field. The vortex is initialised
with the stream function
..math::
\Psi = \frac{1}{4\pi}\sin(4\pi (x+0.5))\sin(4\pi (y+0.5)),
where the velocities are then given by
:math:`u = \partial\Psi/\partial y`,
:math:`v = -\partial\Psi/\partial x`.
The vortex reverses direction after a certain number of timesteps to see
how close the system returns to the initial conditions.
Test found in:
Enright, D.P., 2002. Use of the Particle Level Set Method for Enhanced Resolution of Free Surface Flows. Stanford University. Available at: http://web.stanford.edu/group/fpc/Publications/Enright Thesis.pdf.
"""
# create circle
N = 50
t = 0.
X, Y = np.meshgrid(np.linspace(0., 1., N), np.linspace(0., 1., N))
r = 0.2
dx = 1.0 / (N - 1.)
dy = dx
dt = 0.05
phi = (X - 0.5)**2 + (Y - 0.5)**2 - r**2
phi = computeDistanceFunction(phi, dx)
phi = enforce2dPeriodicBCs(phi)
title = "Distortion field evolution"
print("Initial area enclosed: " + str(enclosedArea(phi, dx, dy)))
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi), title, [0, dx * (N - 4), 0, dx * (N - 4)],
[2, N - 3, 2, N - 3], 0, 0)
plt.show(block=False)
nIt = 200
sL0 = 0.0
marksteinLength = 0.0
u = np.zeros_like(phi)
v = np.zeros_like(phi)
adVel = 0.1 # magnitude of advective velocity
iblims = np.array([2, N - 3, 2, N - 3])
lims = np.array([2, N - 2, 2, N - 2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx * (N - 4), 0, dx * (N - 4)])
# make velocities
u[:, :] = -adVel * np.sin(4. * (Y[:, :] + 0.5) * np.pi) * \
np.sin(4. * (X[:,:] + 0.5) * np.pi)
v[:, :] = -adVel * np.cos(4. * (Y[:, :] + 0.5) * np.pi) * \
np.cos(4. * (X[:,:] + 0.5) * np.pi)
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi,
sL0,
marksteinLength,
u,
v,
iblims,
dx=dx,
dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforce2dPeriodicBCs(Fx)
Fy = enforce2dPeriodicBCs(Fy)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo + 1:ihi + 1, jlo:jhi]) / dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo + 1:jhi + 1]) / dy)
t += dt
# enforce outflow boundary conditions
phi = enforce2dPeriodicBCs(phi)
# plotting
dovis(np.transpose(phi),
title,
gridlims,
iblims,
n,
t,
u=u,
v=v,
area=enclosedArea(phi, dx, dy))
#streamplot(np.linspace(-0.5, 0.5, N), u, v, title)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
# now reverse the direction of the vortex and rewind
u[:, :] = -u[:, :]
v[:, :] = -v[:, :]
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi,
sL0,
marksteinLength,
u,
v,
iblims,
dx=dx,
dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforce2dPeriodicBCs(Fx)
Fy = enforce2dPeriodicBCs(Fy)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo + 1:ihi + 1, jlo:jhi]) / dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo + 1:jhi + 1]) / dy)
t += dt
# enforce periodic boundary conditions
phi = enforce2dPeriodicBCs(phi)
# plotting
dovis(np.transpose(phi),
title,
gridlims,
iblims,
n + nIt,
t,
u=u,
v=v,
area=enclosedArea(phi, dx, dy))
#streamplot(np.linspace(-0.5, 0.5, N), u, v, title)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
print("Final area enclosed: " + str(enclosedArea(phi, dx, dy)))
return
def testSquareEvolution():
r"""
Evolves an initially square level set to see if it remains square.
"""
# create square
N = 80
X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
t = 0.
dx = 2.0 / (N - 1)
dy = dx
dt = 0.1
phi = np.ones((N, N))
phi[N / 2 - 5:N / 2 + 6, N / 2 - 5:N / 2 + 6] = -1.
phi = computeDistanceFunction(phi, dx)
title = "Square evolution"
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi), title, [0, dx * (N - 4), 0, dx * (N - 4)],
[2, N - 3, 2, N - 3], 0, 0)
plt.show(block=False)
nIt = 250
sL0 = 0.0
marksteinLength = 0.0
adVel = 0.05 # magnitude of advective velocity
u = np.zeros_like(phi)
v = np.zeros_like(phi)
iblims = np.array([2, N - 3, 2, N - 3])
lims = np.array([2, N - 2, 2, N - 2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx * (N - 4), 0, dx * (N - 4)])
# make velocities
# rhs
mask = (Y > 0.) * (Y > np.abs(X))
u[mask] = adVel
# lhs
mask = (Y < 0.) * (np.fabs(Y) > np.abs(X))
u[mask] = -1. * adVel
# top
mask = (X > 0.) * (X > np.abs(Y))
v[mask] = adVel
# bottom
mask = (X < 0.) * (np.fabs(X) > np.abs(Y))
v[mask] = -1. * adVel
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi,
sL0,
marksteinLength,
u,
v,
iblims,
dx=dx,
dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforceOutflowBCs(Fx, lims)
Fy = enforceOutflowBCs(Fy, lims)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo + 1:ihi + 1, jlo:jhi]) / dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo + 1:jhi + 1]) / dy)
t += dt
# enforce outflow boundary conditions
phi = enforceOutflowBCs(phi, lims)
# plotting
dovis(phi, title, gridlims, iblims, n, t, u=u, v=v)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
return
def testSineEvolution():
r"""
Evolves level set with periodic boundary conditions.
"""
# create sine
N = 85
sinewidth = np.rint(N / 10)
sinewidth = sinewidth.astype(int)
t = 0.
dx = 2.0 / (N - 5)
dy = dx
dt = 0.1
phi = np.ones((N, N))
phi[N / 2 - sinewidth:N / 2 + sinewidth + 1, :] = -1.
phi = computeDistanceFunction(phi, dx)
title = "Periodic evolution"
toCSV = False
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(phi, title, [0, dx * (N - 5), 0, dx * (N - 5)], [2, N - 3, 2, N - 3],
0, 0)
plt.show(block=False)
nIt = 150
sL0 = 0.08
marksteinLength = 0.05
u = np.ones_like(phi) * 0.08
iblims = np.array([2, N - 3, 2, N - 3])
lims = np.array([2, N - 2, 2, N - 2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx * (N - 5), 0, dx * (N - 5)])
if toCSV:
headers = ['t', 'xcoord', 'ycoord', 'phi']
filepath = \
'/home/alice/Documents/Dropbox/LSMLIB/pylsmlib/pylsmlib/fire/'
xs = [dx * n for n in range(N - 4)]
ys = [dy * n for n in range(N - 4)]
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi,
sL0,
marksteinLength,
u,
u,
iblims,
dx=dx,
dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=u)
Fx = enforcePeriodicBCs(Fx, lims)
Fy = enforcePeriodicBCs(Fy, lims)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo + 1:ihi + 1, jlo:jhi]) / dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo + 1:jhi + 1]) / dy)
t += dt
# enforce periodic boundary conditions
phi[:, :] = enforcePeriodicBCs(phi[:, :], lims)
# plotting
dovis(phi, title, gridlims, iblims, n, t)
plt.show(block=False)
# save to file
if toCSV:
# remember to ignore ghosts
rows = [(t, xs[i], ys[j], phi[i, j]) for j in range(N - 4)
for i in range(N - 4)]
with open(filepath + 'sine' + str(n) + '.csv', 'w') as f:
f_csv = csv.writer(f)
f_csv.writerow(headers)
f_csv.writerows(rows)
# reinitialise
phi[:, :] = computeDistanceFunction(phi[:, :], dx)
return
def testSphereEvolution():
r"""
Evolves an initially spherical set to see if it remains spherical.
"""
# create circle
N = 20
t = 0.
X, Y, Z = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N),
np.linspace(-1, 1, N))
r = 0.3
dx = 2.0 / (N - 1)
dy = dx
dz = dx
dt = 0.1
phi = (X)**2 + (Y)**2 + (Z)**2 - r**2
phi = computeDistanceFunction(phi, dx)
title = "Sphere evolution"
toCSV = False
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi[N / 2, :, :]), title,
[0, dx * (N - 4), 0, dx * (N - 4)], [2, N - 3, 2, N - 3], 0, 0)
plt.show(block=False)
nIt = 100
sL0 = 0.2
marksteinLength = 0.05
u = 0.1 * np.zeros_like(phi)
iblims = np.array([2, N - 3, 2, N - 3, 2, N - 3])
lims = np.array([2, N - 2, 2, N - 2, 2, N - 2])
ilo, ihi, jlo, jhi, klo, khi = lims
# gridlims = np.array([0, dx*(N-4), 0, dx*(N-4), 0, dx*(N-4)])
if toCSV:
headers = ['t', 'xcoord', 'ycoord', 'zcoord', 'phi']
filepath = \
'/home/alice/Documents/Dropbox/LSMLIB/pylsmlib/pylsmlib/fire/'
xs = [dx * n for n in range(N - 4)]
ys = [dy * n for n in range(N - 4)]
zs = [dz * n for n in range(N - 4)]
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed(phi,
sL0,
marksteinLength,
u,
u,
u,
iblims,
dx=dx,
dy=dx,
dz=dz)
# calculate fluxes
Fx, Fy, Fz = findFluxes3d(phi,
sL,
lims,
dx=dx,
dy=dy,
dz=dz,
u=u,
v=u,
w=u)
Fx = enforceOutflowBCs3d(Fx, lims)
Fy = enforceOutflowBCs3d(Fy, lims)
Fz = enforceOutflowBCs3d(Fz, lims)
phi[ilo:ihi, jlo:jhi, klo:khi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi, klo:khi] +
Fx[ilo + 1:ihi + 1, jlo:jhi, klo:khi]) / dx +
(Fy[ilo:ihi, jlo:jhi, klo:khi] +
Fy[ilo:ihi, jlo + 1:jhi + 1, klo:khi]) / dy +
(Fz[ilo:ihi, jlo:jhi, klo:khi] +
Fz[ilo:ihi, jlo:jhi, klo + 1:khi + 1]) / dx)
t += dt
# enforce outflow boundary conditions
phi = enforceOutflowBCs3d(phi, lims)
# plotting
dovis(np.transpose(phi[N / 2, :, :]), title,
[0, dx * (N - 4), 0, dx * (N - 4)], [2, N - 3, 2, N - 3], n, t)
plt.show(block=False)
# save to file
if toCSV:
# remember to ignore ghosts
rows = [(t, xs[i], ys[j], zs[k], phi[i, j, k])
for k in range(N - 4) for j in range(N - 4)
for i in range(N - 4)]
with open(filepath + 'sphere' + str(n) + '.csv', 'w') as f:
f_csv = csv.writer(f)
f_csv.writerow(headers)
f_csv.writerows(rows)
# reinitialise
phi = computeDistanceFunction(phi, dx)
return
def testCircleEvolution():
r"""
Evolves an initially circular level set to see if it remains circular.
"""
# create circle
N = 50
t = 0.
X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
r = 0.3
dx = 2.0 / (N - 1)
dy = dx
dt = 0.1
phi = (X) ** 2 + (Y) ** 2 - r ** 2
phi = computeDistanceFunction(phi, dx)
title = "Circle evolution"
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi), title,
[0, dx*(N-4), 0, dx*(N-4)], [2, N-3, 2, N-3], 0, 0)
plt.show(block=False)
nIt = 200
sL0 = 0.0
marksteinLength = 0.0
u = np.zeros_like(phi)
v = np.zeros_like(phi)
adVel = 0.1 # magnitude of advective velocity
iblims = np.array([2, N-3, 2, N-3])
lims = np.array([2, N-2, 2, N-2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx*(N-4), 0, dx*(N-4)])
# make velocities
hyp = np.sqrt(X[:, :]**2 + Y[:, :]**2)
u[:, :] = adVel * Y[:, :] / hyp[:, :]
v[:, :] = adVel * X[:, :] / hyp[:, :]
# fix signs
u[:N/2, :] = -1. * np.fabs(u[:N/2, :])
u[N/2:, :] = np.fabs(u[N/2:, :])
v[:, :N/2] = -1. * np.fabs(v[:, :N/2])
v[:, N/2:] = np.fabs(v[:, N/2:])
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi, sL0, marksteinLength, u, v,
iblims, dx=dx, dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforceOutflowBCs(Fx, lims)
Fy = enforceOutflowBCs(Fy, lims)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo+1:ihi+1, jlo:jhi])/dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo+1:jhi+1])/dy)
t += dt
# enforce outflow boundary conditions
phi = enforceOutflowBCs(phi, lims)
# plotting
dovis(phi, title, gridlims, iblims, n, t, u=u, v=v)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
return
def testSquareEvolution():
r"""
Evolves an initially square level set to see if it remains square.
"""
# create square
N = 80
X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
t = 0.
dx = 2.0 / (N - 1)
dy = dx
dt = 0.1
phi = np.ones((N, N))
phi[N/2-5:N/2+6, N/2-5:N/2+6] = -1.
phi = computeDistanceFunction(phi, dx)
title = "Square evolution"
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi), title,
[0, dx*(N-4), 0, dx*(N-4)], [2, N-3, 2, N-3], 0, 0)
plt.show(block=False)
nIt = 250
sL0 = 0.0
marksteinLength = 0.0
adVel = 0.05 # magnitude of advective velocity
u = np.zeros_like(phi)
v = np.zeros_like(phi)
iblims = np.array([2, N-3, 2, N-3])
lims = np.array([2, N-2, 2, N-2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx*(N-4), 0, dx*(N-4)])
# make velocities
# rhs
mask = (Y > 0.) * (Y > np.abs(X))
u[mask] = adVel
# lhs
mask = (Y < 0.) * (np.fabs(Y) > np.abs(X))
u[mask] = -1.*adVel
# top
mask = (X > 0.) * (X > np.abs(Y))
v[mask] = adVel
# bottom
mask = (X < 0.) * (np.fabs(X) > np.abs(Y))
v[mask] = -1.*adVel
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi, sL0, marksteinLength, u, v,
iblims, dx=dx, dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforceOutflowBCs(Fx, lims)
Fy = enforceOutflowBCs(Fy, lims)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo+1:ihi+1, jlo:jhi])/dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo+1:jhi+1])/dy)
t += dt
# enforce outflow boundary conditions
phi = enforceOutflowBCs(phi, lims)
# plotting
dovis(phi, title, gridlims, iblims, n, t, u=u, v=v)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
return
def testPeriodicVortexEvolution():
r"""
Evolves a circle in periodic vortex field. The vortex is initialised
with the stream function
..math::
\Psi = \frac{1}{4\pi}\sin(4\pi (x+0.5))\sin(4\pi (y+0.5)),
where the velocities are then given by
:math:`u = \partial\Psi/\partial y`,
:math:`v = -\partial\Psi/\partial x`.
The vortex reverses direction after a certain number of timesteps to see
how close the system returns to the initial conditions.
Test found in:
Enright, D.P., 2002. Use of the Particle Level Set Method for Enhanced Resolution of Free Surface Flows. Stanford University. Available at: http://web.stanford.edu/group/fpc/Publications/Enright Thesis.pdf.
"""
# create circle
N = 50
t = 0.
X, Y = np.meshgrid(np.linspace(0., 1., N), np.linspace(0., 1., N))
r = 0.2
dx = 1.0 / (N - 1.)
dy = dx
dt = 0.05
phi = (X-0.5) ** 2 + (Y-0.5) ** 2 - r ** 2
phi = computeDistanceFunction(phi, dx)
phi = enforce2dPeriodicBCs(phi)
title = "Distortion field evolution"
print("Initial area enclosed: " + str(enclosedArea(phi, dx, dy)))
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi), title,
[0, dx*(N-4), 0, dx*(N-4)], [2, N-3, 2, N-3], 0, 0)
plt.show(block=False)
nIt = 200
sL0 = 0.0
marksteinLength = 0.0
u = np.zeros_like(phi)
v = np.zeros_like(phi)
adVel = 0.1 # magnitude of advective velocity
iblims = np.array([2, N-3, 2, N-3])
lims = np.array([2, N-2, 2, N-2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx*(N-4), 0, dx*(N-4)])
# make velocities
u[:, :] = -adVel * np.sin(4. * (Y[:, :] + 0.5) * np.pi) * \
np.sin(4. * (X[:,:] + 0.5) * np.pi)
v[:, :] = -adVel * np.cos(4. * (Y[:, :] + 0.5) * np.pi) * \
np.cos(4. * (X[:,:] + 0.5) * np.pi)
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi, sL0, marksteinLength, u, v,
iblims, dx=dx, dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforce2dPeriodicBCs(Fx)
Fy = enforce2dPeriodicBCs(Fy)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo+1:ihi+1, jlo:jhi])/dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo+1:jhi+1])/dy)
t += dt
# enforce outflow boundary conditions
phi = enforce2dPeriodicBCs(phi)
# plotting
dovis(np.transpose(phi), title, gridlims, iblims, n, t, u=u, v=v,
area=enclosedArea(phi, dx, dy))
#streamplot(np.linspace(-0.5, 0.5, N), u, v, title)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
# now reverse the direction of the vortex and rewind
u[:, :] = -u[:, :]
v[:, :] = -v[:, :]
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi, sL0, marksteinLength, u, v,
iblims, dx=dx, dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=v)
Fx = enforce2dPeriodicBCs(Fx)
Fy = enforce2dPeriodicBCs(Fy)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo+1:ihi+1, jlo:jhi])/dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo+1:jhi+1])/dy)
t += dt
# enforce periodic boundary conditions
phi = enforce2dPeriodicBCs(phi)
# plotting
dovis(np.transpose(phi), title, gridlims, iblims, n+nIt, t, u=u, v=v,
area=enclosedArea(phi, dx, dy))
#streamplot(np.linspace(-0.5, 0.5, N), u, v, title)
plt.show(block=False)
# reinitialise
phi = computeDistanceFunction(phi, dx)
print("Final area enclosed: " + str(enclosedArea(phi, dx, dy)))
return
def testSphereEvolution():
r"""
Evolves an initially spherical set to see if it remains spherical.
"""
# create circle
N = 20
t = 0.
X, Y, Z = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N),
np.linspace(-1, 1, N))
r = 0.3
dx = 2.0 / (N - 1)
dy = dx
dz = dx
dt = 0.1
phi = (X) ** 2 + (Y) ** 2 + (Z) ** 2 - r ** 2
phi = computeDistanceFunction(phi, dx)
title = "Sphere evolution"
toCSV = False
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(np.transpose(phi[N/2, :, :]), title,
[0, dx*(N-4), 0, dx*(N-4)], [2, N-3, 2, N-3], 0, 0)
plt.show(block=False)
nIt = 100
sL0 = 0.2
marksteinLength = 0.05
u = 0.1 * np.zeros_like(phi)
iblims = np.array([2, N-3, 2, N-3, 2, N-3])
lims = np.array([2, N-2, 2, N-2, 2, N-2])
ilo, ihi, jlo, jhi, klo, khi = lims
# gridlims = np.array([0, dx*(N-4), 0, dx*(N-4), 0, dx*(N-4)])
if toCSV:
headers = ['t', 'xcoord', 'ycoord', 'zcoord', 'phi']
filepath = \
'/home/alice/Documents/Dropbox/LSMLIB/pylsmlib/pylsmlib/fire/'
xs = [dx*n for n in range(N-4)]
ys = [dy*n for n in range(N-4)]
zs = [dz*n for n in range(N-4)]
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed(phi, sL0, marksteinLength, u, u,
u, iblims, dx=dx, dy=dx, dz=dz)
# calculate fluxes
Fx, Fy, Fz = findFluxes3d(phi, sL, lims, dx=dx, dy=dy, dz=dz, u=u,
v=u, w=u)
Fx = enforceOutflowBCs3d(Fx, lims)
Fy = enforceOutflowBCs3d(Fy, lims)
Fz = enforceOutflowBCs3d(Fz, lims)
phi[ilo:ihi, jlo:jhi, klo:khi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi, klo:khi] +
Fx[ilo+1:ihi+1, jlo:jhi, klo:khi]) / dx +
(Fy[ilo:ihi, jlo:jhi, klo:khi] +
Fy[ilo:ihi, jlo+1:jhi+1, klo:khi]) / dy +
(Fz[ilo:ihi, jlo:jhi, klo:khi] +
Fz[ilo:ihi, jlo:jhi, klo+1:khi+1]) / dx)
t += dt
# enforce outflow boundary conditions
phi = enforceOutflowBCs3d(phi, lims)
# plotting
dovis(np.transpose(phi[N/2, :, :]), title,
[0, dx*(N-4), 0, dx*(N-4)], [2, N-3, 2, N-3], n, t)
plt.show(block=False)
# save to file
if toCSV:
# remember to ignore ghosts
rows = [(t, xs[i], ys[j], zs[k], phi[i, j, k]) for k in range(N-4)
for j in range(N-4) for i in range(N-4)]
with open(filepath + 'sphere' + str(n) + '.csv', 'w') as f:
f_csv = csv.writer(f)
f_csv.writerow(headers)
f_csv.writerows(rows)
# reinitialise
phi = computeDistanceFunction(phi, dx)
return
def testSineEvolution():
r"""
Evolves level set with periodic boundary conditions.
"""
# create sine
N = 85
sinewidth = np.rint(N/10)
sinewidth = sinewidth.astype(int)
t = 0.
dx = 2.0 / (N - 5)
dy = dx
dt = 0.1
phi = np.ones((N, N))
phi[N/2-sinewidth:N/2+sinewidth+1, :] = -1.
phi = computeDistanceFunction(phi, dx)
title = "Periodic evolution"
toCSV = False
# set up plot
plt.ion()
plt.figure(num=1, figsize=(12, 9), dpi=100, facecolor='w')
dovis(phi, title, [0, dx*(N-5), 0, dx*(N-5)], [2, N-3, 2, N-3], 0, 0)
plt.show(block=False)
nIt = 150
sL0 = 0.08
marksteinLength = 0.05
u = np.ones_like(phi)*0.08
iblims = np.array([2, N-3, 2, N-3])
lims = np.array([2, N-2, 2, N-2])
ilo, ihi, jlo, jhi = lims
gridlims = np.array([0, dx*(N-5), 0, dx*(N-5)])
if toCSV:
headers = ['t', 'xcoord', 'ycoord', 'phi']
filepath = \
'/home/alice/Documents/Dropbox/LSMLIB/pylsmlib/pylsmlib/fire/'
xs = [dx*n for n in range(N-4)]
ys = [dy*n for n in range(N-4)]
for n in range(nIt):
# flame speed
sL = pythonisedfns.laminarFlameSpeed2d(phi, sL0, marksteinLength, u, u,
iblims, dx=dx, dy=dx)
# calculate fluxes
Fx, Fy = findFluxes(phi, sL, lims, dx=dx, dy=dy, u=u, v=u)
Fx = enforcePeriodicBCs(Fx, lims)
Fy = enforcePeriodicBCs(Fy, lims)
phi[ilo:ihi, jlo:jhi] -= 0.5 * dt * (
(Fx[ilo:ihi, jlo:jhi] + Fx[ilo+1:ihi+1, jlo:jhi])/dx +
(Fy[ilo:ihi, jlo:jhi] + Fy[ilo:ihi, jlo+1:jhi+1])/dy)
t += dt
# enforce periodic boundary conditions
phi[:, :] = enforcePeriodicBCs(phi[:, :], lims)
# plotting
dovis(phi, title, gridlims, iblims, n, t)
plt.show(block=False)
# save to file
if toCSV:
# remember to ignore ghosts
rows = [(t, xs[i], ys[j], phi[i, j]) for j in range(N-4)
for i in range(N-4)]
with open(filepath + 'sine' + str(n) + '.csv', 'w') as f:
f_csv = csv.writer(f)
f_csv.writerow(headers)
f_csv.writerows(rows)
# reinitialise
phi[:, :] = computeDistanceFunction(phi[:, :], dx)
return