def __init__(self,X,Y,Z=array([0,0,0]),coordinates=array([0,0]),velocityTranspose=array([0,0]),dt=.1,gradESquaredTranspose=array([0,0]),fluid=1,forces=1,physConsts=1,repeatX=True,repeatY=False):
self.dt = dt
rx = (repeatX == "True" or repeatX == True)
ry = (repeatY == "True" or repeatY == True)
self.BI = BilinearInterpolation(X,Y,coordinates,velocityTranspose,gradESquaredTranspose,repeatX=rx,repeatY=ry)
self.TI = TrilinearInterpolation(X,Y,Z,coordinates,velocityTranspose,gradESquaredTranspose)
self.fluid = fluid
self.forces = forces
self.physConsts = physConsts
class RungeKuttaIntegrator:
"""2nd Order Runge Kutta Integrator for specific Objects (Tracker,Particle,ParticleAdvanced)
Methods:
tracker : Tracker object with only velocity interpolation
particle : Particle object with stokes and gravitational forces
particleAdvanced : Particle object with stokes, gravitational, and buoyant forces
Attributes:
X : X object data
Y : Y object data
coordinates : np.array([[x1,x2,x3,...],[y1,y2,y3,...]])
velocityTranspose : np.array([[x1,y1],[x2,y2],[x3,y3]...])
dt : time step value
"""
def __init__(self,X,Y,Z=array([0,0,0]),coordinates=array([0,0]),velocityTranspose=array([0,0]),dt=.1,gradESquaredTranspose=array([0,0]),fluid=1,forces=1,physConsts=1,repeatX=True,repeatY=False):
self.dt = dt
rx = (repeatX == "True" or repeatX == True)
ry = (repeatY == "True" or repeatY == True)
self.BI = BilinearInterpolation(X,Y,coordinates,velocityTranspose,gradESquaredTranspose,repeatX=rx,repeatY=ry)
self.TI = TrilinearInterpolation(X,Y,Z,coordinates,velocityTranspose,gradESquaredTranspose)
self.fluid = fluid
self.forces = forces
self.physConsts = physConsts
def tracker(self,tracker):
"""Does not include any force calculations, only velocity tracing"""
#avgVel = self.BI.averageVelocity(tracker.position)
tracker.position = self.BI.checkPointVsBoundaries(point=tracker.position)
nearestIndexes = self.BI.buildNearestIndexes(tracker.position)
avgVel = self.BI.interpolate(point=tracker.position,indexList=nearestIndexes,fieldName='velocity')
posTmp = tracker.position+avgVel*self.dt/2.
posTmp = self.BI.checkPointVsBoundaries(point = posTmp)
nearestIndexes = self.BI.buildNearestIndexes(posTmp)
avgVelTmp = self.BI.interpolate(point=posTmp,indexList=nearestIndexes,fieldName='velocity')
#avgVelTmp = self.BI.averageVelocity(posTmp)
return tracker.position+avgVelTmp*self.dt
def particle(self,particle):
"""2nd order Runge-Kutta integrator for a particle
Args:
particle : Particle object
fluid : Fluid object
forces : Forces object
"""
radius = particle.radius
mass = particle.mass
DEPFactor = particle.DEPFactor
viscosity = self.fluid.viscosity
relativePermittivity = self.fluid.relativePermittivity
chkPvsBnd = self.BI.checkPointVsBoundaries
chkPvsTV = self.checkParticleVsTerminalVelocity
nearInds = self.BI.buildNearestIndexes
interp = self.BI.interpolate
stokes = self.forces.stokes
DEP = self.forces.DEP
dt = self.dt
nearestIndexes = nearInds(particle.position)
avgVel = interp(point=particle.position,indexList=nearestIndexes,fieldName='velocity')
avgEField = interp(point=particle.position,indexList=nearestIndexes,fieldName='Efield')
particle.velocity = chkPvsTV(particleVelocity=particle.velocity,fluidVelocity=avgVel
,DEPFactor=DEPFactor,radius=radius,Efield=avgEField)
relativeVel = avgVel - particle.velocity
sumForces = stokes(radius=radius,relativeVelocity=relativeVel,viscosity=viscosity)+\
DEP(CMFactor=DEPFactor,relativePermittivity=relativePermittivity,radius=radius,gradESquared=avgEField)
acceleration = sumForces/mass
velocityTmp = particle.velocity+acceleration*dt/2
positionTmp = particle.position+particle.velocity*dt/2
positionTmp = chkPvsBnd(point = positionTmp)
nearestIndexes = nearInds(positionTmp)
avgVelTmp = interp(point=positionTmp,indexList=nearestIndexes,fieldName='velocity')
avgEFieldTmp = interp(point=positionTmp,indexList=nearestIndexes,fieldName='Efield')
particle.velocity = chkPvsTV(particleVelocity=velocityTmp,fluidVelocity=avgVelTmp
,DEPFactor=DEPFactor,radius=radius,Efield=avgEFieldTmp)
relativeVelTmp = avgVelTmp - velocityTmp
sumForcesTmp = stokes(radius=radius,relativeVelocity=relativeVelTmp,viscosity=viscosity)+\
DEP(CMFactor=DEPFactor,relativePermittivity=relativePermittivity,radius=radius,gradESquared=avgEFieldTmp)
accelerationTmp = sumForcesTmp/mass
particle.velocity = particle.velocity + accelerationTmp*dt
return chkPvsBnd(point=(particle.position+velocityTmp*dt),obj=particle)
def particle3D(self,particle):
"""2nd order Runge-Kutta integrator for a particle
Args:
particle : Particle object
fluid : Fluid object
forces : Forces object
"""
radius = particle.radius
mass = particle.mass
viscosity = self.fluid.viscosity
#chkPvsBnd = self.TI.checkPointVsBoundaries
chkPvsTV = self.checkParticleVsTerminalVelocity3D
nearInds = self.TI.buildNearestIndexes3D
interp = self.TI.trilinearInterpolation
stokes = self.forces.stokes
dt = self.dt
nearestIndexes = nearInds(particle.position)
avgVel = interp(point=particle.position,indexList=nearestIndexes)
particle.velocity = chkPvsTV(particleVelocity=particle.velocity,fluidVelocity=avgVel)
relativeVel = avgVel - particle.velocity
sumForces = stokes(radius=radius,relativeVelocity=relativeVel,viscosity=viscosity)
acceleration = sumForces/mass
velocityTmp = particle.velocity+acceleration*dt/2
positionTmp = particle.position+particle.velocity*dt/2
#positionTmp = chkPvsBnd(point = positionTmp)
nearestIndexes = nearInds(positionTmp)
avgVelTmp = interp(point=positionTmp,indexList=nearestIndexes)
particle.velocity = chkPvsTV(particleVelocity=velocityTmp,fluidVelocity=avgVelTmp)
relativeVelTmp = avgVelTmp - velocityTmp
sumForcesTmp = stokes(radius=radius,relativeVelocity=relativeVelTmp,viscosity=viscosity)
accelerationTmp = sumForcesTmp/mass
particle.velocity = particle.velocity + accelerationTmp*dt
#return chkPvsBnd(point=(particle.position+velocityTmp*dt),obj=particle)
return particle.position+velocityTmp*dt
def checkParticleVsTerminalVelocity(self,particleVelocity,fluidVelocity,DEPFactor,radius,Efield):
relativePermittivity=self.fluid.relativePermittivity
vacuumPermittivity=self.physConsts.vacuumPermittivity
viscosity=self.fluid.viscosity
terminalVelocity = (DEPFactor*relativePermittivity*vacuumPermittivity*(radius**2)*Efield*((viscosity*3)**-1))+fluidVelocity
if particleVelocity[0] > terminalVelocity[0]:
particleVelocity[0] = terminalVelocity[0]
if particleVelocity[1] > terminalVelocity[1]:
particleVelocity[1] = terminalVelocity[1]
return particleVelocity
def checkParticleVsTerminalVelocity3D(self,particleVelocity,fluidVelocity):
terminalVelocity = fluidVelocity
if particleVelocity[0] > terminalVelocity[0]:
particleVelocity[0] = terminalVelocity[0]
if particleVelocity[1] > terminalVelocity[1]:
particleVelocity[1] = terminalVelocity[1]
if particleVelocity[2] > terminalVelocity[2]:
particleVelocity[2] = terminalVelocity[2]
return particleVelocity
