def plotVel(fieldGens,vinf,BCList,tim):
"""Plots velocity vector plot
Designed to be used with tInt test case 4.
Change for different cases as required"""
plt.figure()
[plt.plot(numpy.array(eachBC.points).transpose()[0],numpy.array(eachBC.points).transpose()[1],linewidth=3.0) for eachBC in BCList]
plt.title('Test Case for RK-2 Viscous Flow Around a Cylinder \n Velocity Plot: Time=%f'%tim)
X,Y = numpy.meshgrid(numpy.arange(0.0,5.0,0.2),numpy.arange(0.0,2.5,0.1))
plt.xlim([-0.1,5.0])
plt.ylim([-0.1,2.5])
pos=numpy.array([X.flatten(),Y.flatten()]).transpose()
# Apply no penetration boundary condition in order to find velocity field
[eachBC.findVcp(fieldGens,vinf) for eachBC in BCList]
[eachBC.applyNPBC(fieldGens) for eachBC in BCList]
Vel = definations.velField(pos,fieldGens,vinf)
[eachBC.closeNPBC(fieldGens) for eachBC in BCList]
# If any point is inside the boundary give it a zero velocity
for j in range(len(pos)):
for eachBC in BCList:
if eachBC.inBoundary(pos[j]):
Vel[j]=numpy.zeros(2)
u=Vel.transpose()[0].reshape(X.shape)
v=Vel.transpose()[1].reshape(X.shape)
plt.quiver(X,Y,u,v)
plt.savefig('Velocity_%f.png'%tim)
return()
def testCylBC1(Np=50):
"""Test cylinder-constant velocity-no penetration boundary condition"""
vinf = numpy.array([10.0, 0.0])
fieldGens = []
toMod = []
#Create cylinder points
rad = 1.0
[points, cpl, normals] = cylBCPoints(rad, Np)
#Add boundary condnitions
BC = wallNPNSBC(points, cpl, normals)
BC.findVcp(fieldGens, vinf)
BC.applyNPBC(fieldGens)
#Define mesh
X, Y = numpy.meshgrid(numpy.arange(-3., 3., 10. / Np),
numpy.arange(-3., 3., 10. / Np))
u = numpy.copy(X)
v = numpy.copy(X)
#Create position array
pos = []
for i in range(len(X.flatten())):
pos.append([X.flatten()[i], Y.flatten()[i]])
pos = numpy.array(pos)
#Calculate field at these positions
F = dfn.velField(pos, fieldGens, vinf)
# Arrange field values in u and v in order to plot them
for i in range(len(X.flatten())):
u.ravel()[i] = F[i][0]
v.ravel()[i] = F[i][1]
if (X.flatten()[i]**2 + Y.flatten()[i]**2 - rad**2) <= 0.2:
u.ravel()[i] = 0.0
v.ravel()[i] = 0.0
BC.closeNPBC(fieldGens)
plt.figure()
plt.quiver(X, Y, u, v)
plt.title('Vector field due to boundary conditions')
plt.plot(
numpy.array(points).transpose()[0],
numpy.array(points).transpose()[1], 'o')
plt.show()
def testCylBC1(Np=50):
"""Test cylinder-constant velocity-no penetration boundary condition"""
vinf=numpy.array([10.0,0.0])
fieldGens=[]
toMod=[]
#Create cylinder points
rad=1.0
[points,cpl,normals]=cylBCPoints(rad,Np)
#Add boundary condnitions
BC=wallNPNSBC(points,cpl,normals)
BC.findVcp(fieldGens,vinf)
BC.applyNPBC(fieldGens)
#Define mesh
X,Y = numpy.meshgrid(numpy.arange(-3.,3.,10./Np),numpy.arange(-3.,3.,10./Np))
u=numpy.copy(X)
v=numpy.copy(X)
#Create position array
pos=[]
for i in range(len(X.flatten())):
pos.append([X.flatten()[i],Y.flatten()[i]])
pos=numpy.array(pos)
#Calculate field at these positions
F=dfn.velField(pos,fieldGens,vinf)
# Arrange field values in u and v in order to plot them
for i in range(len(X.flatten())):
u.ravel()[i]=F[i][0]
v.ravel()[i]=F[i][1]
if (X.flatten()[i]**2+Y.flatten()[i]**2-rad**2)<=0.2:
u.ravel()[i]=0.0
v.ravel()[i]=0.0
BC.closeNPBC(fieldGens)
plt.figure()
plt.quiver(X,Y,u,v)
plt.title('Vector field due to boundary conditions')
plt.plot(numpy.array(points).transpose()[0],numpy.array(points).transpose()[1],'o')
plt.show()
def checkTreeCoeffs():
"""Check whether tree coefficients are properly generated or not. Generates random fieldGens. Find velocities using FMM and regular method, and compares accuracies at different positions"""
# Generate random fieldGens and put them in random lists
fieldGens = randomFieldGens()
# Create random 20 positions; where velocity field will be evaluated
pos = numpy.zeros([20, 2])
for i in range(20):
pos[i][0] = random.random()
pos[i][1] = random.random()
# Find Velocity with regular method
fieldReg = dfn.velField(pos, fieldGens, vinf=0.0)
# Find Velocity with FMM
fieldFMM = velFieldFMM(pos, fieldGens, vinf=0.0)
# Find and print errors between the two
for i in range(20):
err = numpy.norm(fieldReg - fieldFMM)
print err
if err > 1e-06:
print "Error is greater than 1e-06"
def checkTreeCoeffs(): """Check whether tree coefficients are properly generated or not. Generates random fieldGens. Find velocities using FMM and regular method, and compares accuracies at different positions""" # Generate random fieldGens and put them in random lists fieldGens = randomFieldGens() # Create random 20 positions; where velocity field will be evaluated pos = numpy.zeros([20,2]) for i in range(20): pos[i][0] = random.random() pos[i][1] = random.random() # Find Velocity with regular method fieldReg = dfn.velField(pos,fieldGens,vinf = 0.0) # Find Velocity with FMM fieldFMM = velFieldFMM(pos,fieldGens,vinf = 0.0) # Find and print errors between the two for i in range(20): err = numpy.norm(fieldReg - fieldFMM) print err if err > 1e-06: print "Error is greater than 1e-06"
def checkFMMTime():
"""Compare the time taken to calculate velocity fields on each other with varying number of fieldGens"""
Np = [100, 300, 600, 1000, 2000]
tReg = []
tFMM = []
for i in Np:
# Generate random fieldGens and put them in random lists
fieldGens = randomFieldGens(i)
# Calculate pos matrix
N = 0
pos = []
for eachList in fieldGens:
N = N + eachList.nPoints
pos = pos + eachList.posit()
pos = numpy.array(pos)
# Calculate time for regular velocity calculation
initT = time.time()
fieldReg = dfn.velField(pos, fieldGens, vinf=0.)
dt = time.time() - initT
tReg.append(dt)
# Calculate time fot FMM velocity calculation
initT = time.time()
fieldFMM = velFieldFMM(pos, fieldGens, vinf=0.)
dt = time.time() - initT
tFMM.append(dt)
# Plot trends
plt.figure()
plt.plot(Np, tReg, label='Regular')
plt.plot(Np, tFMM, label='FMM')
plt.legend(loc='upper center')
plt.show()
def checkFMMTime(): """Compare the time taken to calculate velocity fields on each other with varying number of fieldGens""" Np = [100,300,600,1000,2000] tReg = [] tFMM = [] for i in Np: # Generate random fieldGens and put them in random lists fieldGens = randomFieldGens(i) # Calculate pos matrix N = 0 pos = [] for eachList in fieldGens: N=N+eachList.nPoints pos=pos+eachList.posit() pos=numpy.array(pos) # Calculate time for regular velocity calculation initT = time.time() fieldReg = dfn.velField(pos,fieldGens,vinf = 0.) dt = time.time() - initT tReg.append(dt) # Calculate time fot FMM velocity calculation initT = time.time() fieldFMM = velFieldFMM(pos,fieldGens,vinf = 0.) dt = time.time() - initT tFMM.append(dt) # Plot trends plt.figure() plt.plot(Np,tReg,label = 'Regular') plt.plot(Np,tFMM,label = 'FMM') plt.legend(loc = 'upper center') plt.show()
def findVcps(self, fieldGens, vinf=0.0):
"""For slip boundary conditions Vcp is to be find slightly above the control point
that is done by using this function. """
self.vcps = dfn.velField(self.cps, fieldGens, vinf)
def findVcp(self, fieldGens=[], vinf=0.0):
"""find V at control points.
This step is to be executed at starting of each step"""
self.vcp = dfn.velField(self.cp, fieldGens, vinf)
def advectRK2(dt,
toMod=[dfn.vortexList(), dfn.traceList()],
fieldGens=[dfn.vortexList(), dfn.linVortList()],
vinf=0.0,
BCList=[]):
"""Modify "toMod(List format)" objects according to RK 2 advection based on fieldGens(List format) for advection"""
#Calculate total number of toMod Points and append their positions
N = 0
pos = []
for eachList in toMod:
N = N + eachList.nPoints
pos = pos + eachList.posit()
pos = numpy.array(pos)
oldPos = pos.copy()
# Satisfy no penetration
[eachBC.findVcp(fieldGens, vinf) for eachBC in BCList]
[eachBC.applyNPBC(fieldGens) for eachBC in BCList]
#Calculate no slip velocities
[eachBC.findVcps(fieldGens, vinf) for eachBC in BCList]
# Calculate field at all positions
field = dfn.velField(pos, fieldGens, vinf)
# Close NP BC
[eachBC.closeNPBC(fieldGens) for eachBC in BCList]
#Take first step of RK 2 and modify positions
n = 0
for eachList in toMod:
for eachPoint in eachList.allV:
newPos = dfn.eulerInt(pos[n], field[n], dt / 2.0)
eachPoint.modifyPos(
newPos
) # Note that this step will also modify appropriate positions in fieldGens, because of pointers
n = n + 1
#Calculate total number of toMod Points and append their positions
newN = 0
pos = []
for eachList in toMod:
newN = newN + eachList.nPoints
pos = pos + eachList.posit()
pos = numpy.array(pos)
if newN != N:
print "number of points cannot change in an advection step"
# Satisfy no penetration
[eachBC.findVcp(fieldGens, vinf) for eachBC in BCList]
[eachBC.applyNPBC(fieldGens) for eachBC in BCList]
#Calculate field with new positions
field = dfn.velField(pos, fieldGens, vinf)
# Close NP BC
[eachBC.closeNPBC(fieldGens) for eachBC in BCList]
# Take second step of RK 2 and modify final positions
n = 0
for eachList in toMod:
for eachPoint in eachList.allV:
newPos = dfn.eulerInt(oldPos[n], field[n], dt)
dPos = newPos - oldPos[n]
#Reflect the new position if it is in boundary
for eachBC in BCList:
if (eachBC.inBoundary(newPos)):
newPos = eachBC.reflect(oldPos[n], dPos)
eachPoint.modifyPos(newPos)
n = n + 1
def advectRK2(dt,toMod=[dfn.vortexList(),dfn.traceList()],fieldGens=[dfn.vortexList(),dfn.linVortList()],vinf=0.0,BCList=[]):
"""Modify "toMod(List format)" objects according to RK 2 advection based on fieldGens(List format) for advection"""
#Calculate total number of toMod Points and append their positions
N=0
pos=[]
for eachList in toMod:
N=N+eachList.nPoints
pos=pos+eachList.posit()
pos=numpy.array(pos)
oldPos=pos.copy()
# Satisfy no penetration
[eachBC.findVcp(fieldGens,vinf) for eachBC in BCList]
[eachBC.applyNPBC(fieldGens) for eachBC in BCList]
#Calculate no slip velocities
[eachBC.findVcps(fieldGens,vinf) for eachBC in BCList]
# Calculate field at all positions
field=dfn.velField(pos,fieldGens,vinf)
# Close NP BC
[eachBC.closeNPBC(fieldGens) for eachBC in BCList]
#Take first step of RK 2 and modify positions
n=0
for eachList in toMod:
for eachPoint in eachList.allV:
newPos=dfn.eulerInt(pos[n],field[n],dt/2.0)
eachPoint.modifyPos(newPos) # Note that this step will also modify appropriate positions in fieldGens, because of pointers
n=n+1
#Calculate total number of toMod Points and append their positions
newN=0
pos=[]
for eachList in toMod:
newN=newN+eachList.nPoints
pos=pos+eachList.posit()
pos=numpy.array(pos)
if newN!=N:
print "number of points cannot change in an advection step"
# Satisfy no penetration
[eachBC.findVcp(fieldGens,vinf) for eachBC in BCList]
[eachBC.applyNPBC(fieldGens) for eachBC in BCList]
#Calculate field with new positions
field=dfn.velField(pos,fieldGens,vinf)
# Close NP BC
[eachBC.closeNPBC(fieldGens) for eachBC in BCList]
# Take second step of RK 2 and modify final positions
n=0
for eachList in toMod:
for eachPoint in eachList.allV:
newPos=dfn.eulerInt(oldPos[n],field[n],dt)
dPos=newPos-oldPos[n]
#Reflect the new position if it is in boundary
for eachBC in BCList:
if (eachBC.inBoundary(newPos)):
newPos=eachBC.reflect(oldPos[n],dPos)
eachPoint.modifyPos(newPos)
n=n+1
def findVcps(self,fieldGens,vinf=0.0): """For slip boundary conditions Vcp is to be find slightly above the control point that is done by using this function. """ self.vcps=dfn.velField(self.cps,fieldGens,vinf)
def findVcp(self,fieldGens=[],vinf=0.0): """find V at control points. This step is to be executed at starting of each step""" self.vcp=dfn.velField(self.cp,fieldGens,vinf)
