def applyRVM(dt, nu=0.1, toMod=[dfn.vortexList(), dfn.traceList()], BCList=[]):
"""Apply RVM diffusion based on kinematic viscocity nu on "toMod" list of lists
Also, reflect any vortex which is getting diffused into the boundary"""
#Calculate mu and sigma for random number generation gaussian distribution
mu = 0.0
sigma = (2 * nu * dt)**0.5
#Modify position for each point
for eachList in toMod:
#Diffusion should not be applied on tracers. This is only for vortex lists. check that condition
if eachList.__class__.__name__ == 'vortexList':
for eachPoint in eachList.allV:
rad = random.gauss(mu, sigma)
theta = random.uniform(-math.pi, math.pi)
dPos = numpy.array(
[rad * math.cos(theta), rad * math.sin(theta)])
newPos = eachPoint.position + dPos
#Reflect the new position if it is in boundary
for eachBC in BCList:
if (eachBC.inBoundary(newPos)):
newPos = eachBC.reflect(eachPoint.position, dPos)
eachPoint.modifyPos(
newPos) #This will also change fieldGen point positions
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 testRVM(cpos=numpy.array([1., 1.]), Np=100):
""" Test RVM diffusion function"""
#Initiate vortex list and tracer list and toMod
V1 = dfn.vortexList()
T1 = dfn.traceList()
toMod = [V1, T1]
#Add points at the same location
for i in range(Np):
V1.addVortex(cpos, 0.1)
#Add arbitary tracers, just for check
T1.addTracer(numpy.array([.5, .5]) + cpos)
T1.addTracer(numpy.array([.5, -.5]) + cpos)
T1.addTracer(numpy.array([-.5, .5]) + cpos)
T1.addTracer(numpy.array([-.5, -.5]) + cpos)
#Apply RVM
dt = 0.1
nu = 0.1
applyRVM(dt, nu, toMod)
#Positions of all points in toMod
pos = []
for eachList in toMod:
pos = pos + eachList.posit()
pos = numpy.array(pos)
#Plot all points. Red is the original vortex, Blue is new distribution
plt.figure()
plt.title("Random vortex method diffusion test")
for i in range(len(pos)):
plt.plot(pos[i][0], pos[i][1], 'bo', markersize=2.0)
plt.plot(cpos[0], cpos[1], 'ro', markersize=4.0)
plt.show()
return ()
def testRVM(cpos=numpy.array([1.,1.]),Np=100):
""" Test RVM diffusion function"""
#Initiate vortex list and tracer list and toMod
V1=dfn.vortexList()
T1=dfn.traceList()
toMod=[V1,T1]
#Add points at the same location
for i in range(Np):
V1.addVortex(cpos,0.1)
#Add arbitary tracers, just for check
T1.addTracer(numpy.array([.5,.5])+cpos)
T1.addTracer(numpy.array([.5,-.5])+cpos)
T1.addTracer(numpy.array([-.5,.5])+cpos)
T1.addTracer(numpy.array([-.5,-.5])+cpos)
#Apply RVM
dt=0.1
nu=0.1
applyRVM(dt,nu,toMod)
#Positions of all points in toMod
pos=[]
for eachList in toMod:
pos=pos+eachList.posit()
pos=numpy.array(pos)
#Plot all points. Red is the original vortex, Blue is new distribution
plt.figure()
plt.title("Random vortex method diffusion test")
for i in range(len(pos)):
plt.plot(pos[i][0],pos[i][1],'bo',markersize=2.0)
plt.plot(cpos[0],cpos[1],'ro',markersize=4.0)
plt.show()
return()
def applyRVM(dt,nu=0.1,toMod=[dfn.vortexList(),dfn.traceList()],BCList=[]): """Apply RVM diffusion based on kinematic viscocity nu on "toMod" list of lists Also, reflect any vortex which is getting diffused into the boundary""" #Calculate mu and sigma for random number generation gaussian distribution mu=0.0 sigma=(2*nu*dt)**0.5 #Modify position for each point for eachList in toMod: #Diffusion should not be applied on tracers. This is only for vortex lists. check that condition if eachList.__class__.__name__=='vortexList': for eachPoint in eachList.allV: rad=random.gauss(mu,sigma) theta=random.uniform(-math.pi,math.pi) dPos=numpy.array([rad*math.cos(theta),rad*math.sin(theta)]) newPos=eachPoint.position+dPos #Reflect the new position if it is in boundary for eachBC in BCList: if (eachBC.inBoundary(newPos)): newPos=eachBC.reflect(eachPoint.position,dPos) eachPoint.modifyPos(newPos) #This will also change fieldGen point positions return()
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