def test4RK2(Npanels=50):
"""Test RK-2 time integrator with boundary conditions. Simulate a Viscous flow around a cylinder.
NPoins being number of tracer points and NPanels being number of panels on the cylinder surface"""
#Define parameters
Re = 1000
delta = (1. / Re)**0.5
lemda = delta * math.pi
gmin = 0.2
#Define V_Infinite, field generators and modifiable points
vinf = numpy.array([1.0, 0.0])
fieldGens = []
toMod = []
#Create cylinder points for boundary conditions
rad = 1.0
[BCpoints, BCcp, BCNormals, BCinFunction,
BCreflectFunction] = wallBC.cylBCPoints(rad, Npanels)
# Viscocity
nu = ((vinf.dot(vinf))**0.5) * 2 * rad / Re
#Initiate boundary condnitions
BCList = []
BC = wallBC.wallNPNSBC(BCpoints, BCcp, BCNormals, BCinFunction,
BCreflectFunction)
BCList.append(BC)
# Initiate time mesh
startTime = 0.0
CFL = 1.0
timeStep = CFL * lemda / ((vinf.dot(vinf))**0.5)
endTime = 6.0
timeMesh = dfn.linearTimeMesh(startTime, timeStep, endTime)
#Start time loop
for i in range(1, len(timeMesh)):
print "time=%f" % timeMesh[i]
dt = timeMesh[i] - timeMesh[i - 1]
# Advect particles
advectRK2(dt, toMod, fieldGens, vinf, BCList)
# Introduce no slip boundary conditions
# Vslips are calculated in the advection step. That is to be changed for better architecture
[eachBC.applyNSBC(fieldGens, toMod, gmin, delta) for eachBC in BCList]
#Diffuse all particles using RVM
diffusion.applyRVM(dt, nu, toMod, BCList)
# Post Processing: to be done after 5 time steps
if i % 5 == 0:
# Plot Vorticity Particles
plots.plotVort(toMod, BCList, timeMesh[i])
# Plot Velocity Field
plots.plotVel(fieldGens, vinf, BCList, timeMesh[i])
return ()
def test1RK2(endTime=100.):
"""A test case for advection RK-2 integrator without any boundaries . Take two vortices of same strength. They should rotate in a circle"""
#Initiate vortex list
VList = dfn.vortexList()
# Define vortices
p1 = numpy.array([-0.5, 0.0])
p2 = numpy.array([0.5, 0.0])
rad = 0.5
VList.addVortex(position=p1,
strength=1.0,
blobType=0,
delta=0.0,
traceFlag=1)
VList.addVortex(position=p2,
strength=1.0,
blobType=0,
delta=0.0,
traceFlag=1)
# Initiate time mesh
startTime = 0.0
timeStep = 0.01
timeMesh = dfn.linearTimeMesh(startTime, timeStep, endTime)
#Start time loop
for i in range(1, len(timeMesh)):
print "time=%f" % timeMesh[i]
dt = timeMesh[i] - timeMesh[i - 1]
advectRK2(dt, toMod=[VList], fieldGens=[VList], vinf=0.0)
#Plot traces of particles
plt.figure(1)
plt.title('test case for RK-2 two particle motion in a circle')
for i in range(VList.nPoints):
plt.plot(
numpy.array(VList.allV[i].traceHist).transpose()[0],
numpy.array(VList.allV[i].traceHist).transpose()[1])
#Calculate Error history
newPos1 = VList.allV[0].traceHist
newPos2 = VList.allV[0].traceHist
err1 = [
abs(newPos1[i].dot(newPos1[i]) - rad**2) for i in range(len(newPos1))
]
err2 = [
abs(newPos2[i].dot(newPos2[i]) - rad**2) for i in range(len(newPos2))
]
#Plot errors
plt.figure(2)
plt.title('errors with time')
plt.plot(err1)
plt.plot(err2)
return ()
def test4RK2(Npanels=50): """Test RK-2 time integrator with boundary conditions. Simulate a Viscous flow around a cylinder. NPoins being number of tracer points and NPanels being number of panels on the cylinder surface""" #Define parameters Re=1000 delta=(1./Re)**0.5 lemda=delta*math.pi gmin=0.2 #Define V_Infinite, field generators and modifiable points vinf=numpy.array([1.0,0.0]) fieldGens=[] toMod=[] #Create cylinder points for boundary conditions rad=1.0 [BCpoints,BCcp,BCNormals,BCinFunction,BCreflectFunction]=wallBC.cylBCPoints(rad,Npanels) # Viscocity nu=((vinf.dot(vinf))**0.5)*2*rad/Re #Initiate boundary condnitions BCList=[] BC=wallBC.wallNPNSBC(BCpoints,BCcp,BCNormals,BCinFunction,BCreflectFunction) BCList.append(BC) # Initiate time mesh startTime=0.0 CFL=1.0 timeStep=CFL*lemda/((vinf.dot(vinf))**0.5) endTime=6.0 timeMesh=dfn.linearTimeMesh(startTime,timeStep,endTime) #Start time loop for i in range(1,len(timeMesh)): print "time=%f"%timeMesh[i] dt=timeMesh[i]-timeMesh[i-1] # Advect particles advectRK2(dt,toMod,fieldGens,vinf,BCList) # Introduce no slip boundary conditions # Vslips are calculated in the advection step. That is to be changed for better architecture [eachBC.applyNSBC(fieldGens,toMod,gmin,delta) for eachBC in BCList] #Diffuse all particles using RVM diffusion.applyRVM(dt,nu,toMod,BCList) # Post Processing: to be done after 5 time steps if i%5==0: # Plot Vorticity Particles plots.plotVort(toMod,BCList,timeMesh[i]) # Plot Velocity Field plots.plotVel(fieldGens,vinf,BCList,timeMesh[i]) return()
def test3RK2(Npanels=50):
"""Compute the motion of a single point vortex at a distance of 1.5 units from the center of the cylinder and plot its trajectory"""
#Define V_Infinite, field generators and modifiable points
vinf = numpy.array([0.0, 0.0])
fieldGens = []
toMod = []
#Define vortex points
VList = dfn.vortexList()
pos = numpy.array([0.0, 1.1])
VList.addVortex(position=pos,
strength=1.0,
blobType=1,
delta=0.1,
traceFlag=1)
toMod.append(VList)
fieldGens.append(VList)
#Create cylinder points for boundary conditions
rad = 1.0
[BCpoints, BCcp, BCNormals, iF, rF] = wallBC.cylBCPoints(rad, Npanels)
#Initiate boundary condnitions
BCList = []
BC = wallBC.wallNPNSBC(BCpoints, BCcp, BCNormals, iF, rF)
BCList.append(BC)
# Initiate time mesh
startTime = 0.0
timeStep = 0.08
endTime = 100.0
timeMesh = dfn.linearTimeMesh(startTime, timeStep, endTime)
#Start time loop
for i in range(1, len(timeMesh)):
print "time=%f" % timeMesh[i]
dt = timeMesh[i] - timeMesh[i - 1]
advectRK2(dt, toMod, fieldGens, vinf, BCList)
#Plot traces of particles
plt.figure(1)
plt.title('Assignment 3 Problem 3')
plt.plot(numpy.array(BCpoints).transpose()[0],
numpy.array(BCpoints).transpose()[1],
linewidth=3.0)
for i in range(VList.nPoints):
plt.plot(
numpy.array(VList.allV[i].traceHist).transpose()[0],
numpy.array(VList.allV[i].traceHist).transpose()[1])
plt.show()
return ()
def test2RK2(Npoints=30, Npanels=50):
"""Test RK-2 time integrator with boundary conditions. Simulate a non-viscous flow around a cylinder.
NPoins being number of tracer points and NPanels being number of panels on the cylinder surface"""
#Define V_Infinite, field generators and modifiable points
vinf = numpy.array([1.0, 0.0])
fieldGens = []
toMod = []
#Define tracer points
TList = dfn.traceList()
lowLim = numpy.array([-5.0, -2.0])
upLim = numpy.array([-5.0, 2.0])
for i in range(Npoints):
pos = (lowLim + (float(i) / Npoints * (upLim - lowLim)))
TList.addTracer(pos, traceFlag=1)
toMod.append(TList)
#Create cylinder points for boundary conditions
rad = 1.0
[BCpoints, BCcp, BCNormals, iF, rF] = wallBC.cylBCPoints(rad, Npanels)
#Initiate boundary condnitions
BCList = []
BC = wallBC.wallNPNSBC(BCpoints, BCcp, BCNormals, iF, rF)
BCList.append(BC)
# Initiate time mesh
startTime = 0.0
timeStep = 0.08
endTime = 10.0
timeMesh = dfn.linearTimeMesh(startTime, timeStep, endTime)
#Start time loop
for i in range(1, len(timeMesh)):
print "time=%f" % timeMesh[i]
dt = timeMesh[i] - timeMesh[i - 1]
advectRK2(dt, toMod, fieldGens, vinf, BCList)
#Plot traces of particles
plt.figure(1)
plt.title('test case for RK-2 non-viscous flow around a cylinder')
plt.plot(numpy.array(BCpoints).transpose()[0],
numpy.array(BCpoints).transpose()[1],
linewidth=3.0)
for i in range(TList.nPoints):
plt.plot(
numpy.array(TList.allV[i].traceHist).transpose()[0],
numpy.array(TList.allV[i].traceHist).transpose()[1])
return ()
def test2RK2(Npoints=30,Npanels=50):
"""Test RK-2 time integrator with boundary conditions. Simulate a non-viscous flow around a cylinder.
NPoins being number of tracer points and NPanels being number of panels on the cylinder surface"""
#Define V_Infinite, field generators and modifiable points
vinf=numpy.array([1.0,0.0])
fieldGens=[]
toMod=[]
#Define tracer points
TList=dfn.traceList()
lowLim=numpy.array([-5.0,-2.0])
upLim=numpy.array([-5.0,2.0])
for i in range(Npoints):
pos=(lowLim+(float(i)/Npoints*(upLim-lowLim)))
TList.addTracer(pos,traceFlag=1)
toMod.append(TList)
#Create cylinder points for boundary conditions
rad=1.0
[BCpoints,BCcp,BCNormals,iF,rF]=wallBC.cylBCPoints(rad,Npanels)
#Initiate boundary condnitions
BCList=[]
BC=wallBC.wallNPNSBC(BCpoints,BCcp,BCNormals,iF,rF)
BCList.append(BC)
# Initiate time mesh
startTime=0.0
timeStep=0.08
endTime=10.0
timeMesh=dfn.linearTimeMesh(startTime,timeStep,endTime)
#Start time loop
for i in range(1,len(timeMesh)):
print "time=%f"%timeMesh[i]
dt=timeMesh[i]-timeMesh[i-1]
advectRK2(dt,toMod,fieldGens,vinf,BCList)
#Plot traces of particles
plt.figure(1)
plt.title('test case for RK-2 non-viscous flow around a cylinder')
plt.plot(numpy.array(BCpoints).transpose()[0],numpy.array(BCpoints).transpose()[1],linewidth=3.0)
for i in range(TList.nPoints):
plt.plot(numpy.array(TList.allV[i].traceHist).transpose()[0],numpy.array(TList.allV[i].traceHist).transpose()[1])
return()
def test3RK2(Npanels=50):
"""Compute the motion of a single point vortex at a distance of 1.5 units from the center of the cylinder and plot its trajectory"""
#Define V_Infinite, field generators and modifiable points
vinf=numpy.array([0.0,0.0])
fieldGens=[]
toMod=[]
#Define vortex points
VList=dfn.vortexList()
pos=numpy.array([0.0,1.1])
VList.addVortex(position=pos,strength=1.0,blobType=1,delta=0.1,traceFlag=1)
toMod.append(VList)
fieldGens.append(VList)
#Create cylinder points for boundary conditions
rad=1.0
[BCpoints,BCcp,BCNormals,iF,rF]=wallBC.cylBCPoints(rad,Npanels)
#Initiate boundary condnitions
BCList=[]
BC=wallBC.wallNPNSBC(BCpoints,BCcp,BCNormals,iF,rF)
BCList.append(BC)
# Initiate time mesh
startTime=0.0
timeStep=0.08
endTime=100.0
timeMesh=dfn.linearTimeMesh(startTime,timeStep,endTime)
#Start time loop
for i in range(1,len(timeMesh)):
print "time=%f"%timeMesh[i]
dt=timeMesh[i]-timeMesh[i-1]
advectRK2(dt,toMod,fieldGens,vinf,BCList)
#Plot traces of particles
plt.figure(1)
plt.title('Assignment 3 Problem 3')
plt.plot(numpy.array(BCpoints).transpose()[0],numpy.array(BCpoints).transpose()[1],linewidth=3.0)
for i in range(VList.nPoints):
plt.plot(numpy.array(VList.allV[i].traceHist).transpose()[0],numpy.array(VList.allV[i].traceHist).transpose()[1])
plt.show()
return()
def test1RK2(endTime=100.):
"""A test case for advection RK-2 integrator without any boundaries . Take two vortices of same strength. They should rotate in a circle"""
#Initiate vortex list
VList=dfn.vortexList()
# Define vortices
p1=numpy.array([-0.5,0.0])
p2=numpy.array([0.5,0.0])
rad=0.5
VList.addVortex(position=p1, strength=1.0,blobType=0,delta=0.0,traceFlag=1)
VList.addVortex(position=p2, strength=1.0,blobType=0,delta=0.0,traceFlag=1)
# Initiate time mesh
startTime=0.0
timeStep=0.01
timeMesh=dfn.linearTimeMesh(startTime,timeStep,endTime)
#Start time loop
for i in range(1,len(timeMesh)):
print "time=%f"%timeMesh[i]
dt=timeMesh[i]-timeMesh[i-1]
advectRK2(dt,toMod=[VList],fieldGens=[VList],vinf=0.0)
#Plot traces of particles
plt.figure(1)
plt.title('test case for RK-2 two particle motion in a circle')
for i in range(VList.nPoints):
plt.plot(numpy.array(VList.allV[i].traceHist).transpose()[0],numpy.array(VList.allV[i].traceHist).transpose()[1])
#Calculate Error history
newPos1=VList.allV[0].traceHist
newPos2=VList.allV[0].traceHist
err1=[abs(newPos1[i].dot(newPos1[i])-rad**2) for i in range(len(newPos1))]
err2=[abs(newPos2[i].dot(newPos2[i])-rad**2) for i in range(len(newPos2))]
#Plot errors
plt.figure(2)
plt.title('errors with time')
plt.plot(err1)
plt.plot(err2)
return()