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fixing indentation #1

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283 changes: 148 additions & 135 deletions TwoDHeat.py
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Original file line number Diff line number Diff line change
@@ -1,135 +1,148 @@
import numpy as np
import matplotlib.animation as ani
import matplotlib.pyplot as plt
from matplotlib.pyplot import imshow, show, colorbar
class TwoDHeatTransfer: #simulates transient 2d heat conduction using ADI method
def __init__(self,parameters):
"""parameters ={
"Length" :
"T0" :
"Tin" :
"alpha" :
"Nelements" :
"timestep" :
"spacestep" :
"Niteration" :
}"""
self.L = parameters["Length"]
self.T0 = parameters["T0"]
self.Tin = parameters["Tin"]
self.alpha = parameters["alpha"]
self.N = parameters["Nelements"]
self.dt = parameters["timestep"]
self.dx = round(parameters["Length"]/parameters["Nelements"],1)
self.nit = parameters["Niteration"]
self.r = self.dt/(self.dx * self.dx) #varaiables handy while the TDM method
self.b = 2*(1/self.r+1) #varaiables handy while the TDM method
self.f = 2*(1/self.r-1) #varaiables handy while the TDM method
def formMatrix(self,d,N): #forms matrix which arises as result of Alternating Directional Implicit method
A=np.zeros((N,N)) # [ b -2 ]
b=self.b # [-1 b -1 ]
for k in range(0,N): # [ -1 b -1 ]
A[k][k]=b # [ -1 b -1 ]
if(k==0): # [ -1 b -1 ]
A[k][k+1]=-2 # [ -1 b -1]
continue # [ -1 b]
A[k][k-1]=-1
if(k!=N-1):
A[k][k+1]=-1
return self.TDMA(A,d)
def updatevalue(self,A,B,N): #just copies values of one array onto other
for i in range(0,N):
for j in range(0,N):
A[i][j]=B[i][j]
def dirichelet(self,thetha,N): #assigns dirichelet boundary condition of thetha = 1 at boundaries
for x in range(0,N+1):
thetha[N][x]=1
thetha[x][N]=1
def TDMA(self,A,b): #solve Ax = b using TDM algorithm
p=[]
q=[]
p.append(-1*A[0][1]/A[0][0])
q.append(b[0]/A[0][0])
x=np.zeros(len(b))
for i in range(1,len(b)):
if i!= len(b)-1:
p.append(-1*A[i][i+1]/(A[i][i]+A[i][i-1]*p[i-1]))
q.append((b[i]-A[i][i-1]*q[i-1])/(A[i][i]+A[i][i-1]*p[i-1]))
x[len(b)-1]=q[len(b)-1]
for i in range(len(b)-2,-1,-1):
x[i]=p[i]*x[i+1]+q[i]
return x
def Halfstepi(self,thetha): #Implicit iteration over x-coordinate
N=self.N
f=self.f
j=0
d=[]
thethastar=np.full((N+1,N+1),0,dtype='f')
for i in range(0,N-1):
d.append(2*thetha[i][j+1]+f*thetha[i][j])
d.append(2*thetha[N-1][j+1]+f*thetha[N-1][j]+thetha[N][j])
u=self.formMatrix(d,N)
for i in range(0,N):
thethastar[i][j]=u[i]
for j in range(1,N):
d=[]
for i in range(0,N-1):
d.append(thetha[i][j-1]+f*thetha[i][j]+thetha[i][j+1])
d.append(thetha[N-1][j-1]+f*thetha[N-1][j]+thetha[N][j+1]+thetha[N][j])
u=self.formMatrix(d,N)
for i in range(0,N):
thethastar[i][j]=u[i]
return thethastar
def Halfstepj(self,thetha): #Implicit iteration over y-coordinate
N=self.N
f=self.f
i=0
d=[]
thethastar=np.full((N+1,N+1),0,dtype='f')
for j in range(0,N-1):
d.append(2*thetha[i+1][j]+f*thetha[i][j])
d.append(2*thetha[i+1][N-1]+f*thetha[i][N-1]+thetha[i][N])
u=self.formMatrix(d,N)
for j in range(0,N):
thethastar[i][j]=u[j]
for i in range(1,N):
d=[]
for j in range(0,N-1):
d.append(thetha[i-1][j]+f*thetha[i][j]+thetha[i+1][j])
d.append(thetha[i-1][N-1]+f*thetha[i][N-1]+thetha[i+1][N]+thetha[i][N])
u=self.formMatrix(d,N)
for j in range(0,N):
thethastar[i][j]=u[j]
return thethastar
def extendsquare(self,A,N): #Extended the matrix in all direction(Symmetry)
box=np.full((2*N-1,2*N-1),0,dtype='f')
for i in range(0,N):
for j in range(0,N):
box[N-1-i][N-1-j]=A[i][j]
box[N-1-i][N-1+j]=A[i][j]
box[N-1+i][N-1-j]=A[i][j]
box[N-1+i][N-1+j]=A[i][j]
return box
def solve(self): #Simulates the diffusion using ADI method
N=self.N
fig = plt.figure()
ax = fig.add_subplot(111)
thetha=np.full((N+1,N+1),0,dtype='f') #Dimensionless temperature
ims=[] #stores thetha at different timesteps later used to visualise
im=imshow(self.extendsquare(thetha,N+1),animated=True)
ims.append([im])
self.dirichelet(thetha,N)
for t in range(self.nit): #time marching
thethastar=self.Halfstepi(thetha) #updates thetha after half time step
self.updatevalue(thetha,thethastar,N)
thethastar=self.Halfstepj(thetha)
self.updatevalue(thetha,thethastar,N) #updates thetha after second half time step
box=self.extendsquare(thetha,N+1)
temp=int(thetha[0][0]*(self.T0-self.Tin)+self.Tin) #next three lines are for the showing timestep and temperature
time = plt.text(0.1, 0.1, "Timestep: "+str(t), horizontalalignment='left', verticalalignment='top', transform=ax.transAxes)
temp = ax.text(0.98,0.95, "Core Temperature: "+str(temp)+"K", horizontalalignment='right', verticalalignment='top', transform=ax.transAxes)
im=imshow(box,vmin=0,vmax=1,animated=True)
if t % 2==0: #only visualising at every other time step
ims.append([im,time,temp])
anim =ani.ArtistAnimation(fig, ims, blit=True,interval=600,repeat_delay=10)
show()
import numpy as np
import matplotlib.animation as ani
import matplotlib.pyplot as plt
from matplotlib.pyplot import imshow, show, colorbar


class TwoDHeatTransfer: # simulates transient 2d heat conduction using ADI method
def __init__(self, parameters):
"""parameters ={
"Length" :
"T0" :
"Tin" :
"alpha" :
"Nelements" :
"timestep" :
"spacestep" :
"Niteration" :
}"""
self.L = parameters["Length"]
self.T0 = parameters["T0"]
self.Tin = parameters["Tin"]
self.alpha = parameters["alpha"]
self.N = parameters["Nelements"]
self.dt = parameters["timestep"]
self.dx = round(parameters["Length"] / parameters["Nelements"], 1)
self.nit = parameters["Niteration"]
self.r = self.dt / (self.dx * self.dx) # varaiables handy while the TDM method
self.b = 2 * (1 / self.r + 1) # varaiables handy while the TDM method
self.f = 2 * (1 / self.r - 1) # varaiables handy while the TDM method

def formMatrix(self, d, N): # forms matrix which arises as result of Alternating Directional Implicit method
A = np.zeros((N, N)) # [ b -2 ]
b = self.b # [-1 b -1 ]
for k in range(0, N): # [ -1 b -1 ]
A[k][k] = b # [ -1 b -1 ]
if (k == 0): # [ -1 b -1 ]
A[k][k + 1] = -2 # [ -1 b -1]
continue # [ -1 b]
A[k][k - 1] = -1
if (k != N - 1):
A[k][k + 1] = -1
return self.TDMA(A, d)

def updatevalue(self, A, B, N): # just copies values of one array onto other
for i in range(0, N):
for j in range(0, N):
A[i][j] = B[i][j]

def dirichelet(self, thetha, N): # assigns dirichelet boundary condition of thetha = 1 at boundaries
for x in range(0, N + 1):
thetha[N][x] = 1
thetha[x][N] = 1

def TDMA(self, A, b): # solve Ax = b using TDM algorithm
p = []
q = []
p.append(-1 * A[0][1] / A[0][0])
q.append(b[0] / A[0][0])
x = np.zeros(len(b))
for i in range(1, len(b)):
if i != len(b) - 1:
p.append(-1 * A[i][i + 1] / (A[i][i] + A[i][i - 1] * p[i - 1]))
q.append((b[i] - A[i][i - 1] * q[i - 1]) / (A[i][i] + A[i][i - 1] * p[i - 1]))
x[len(b) - 1] = q[len(b) - 1]
for i in range(len(b) - 2, -1, -1):
x[i] = p[i] * x[i + 1] + q[i]
return x

def Halfstepi(self, thetha): # Implicit iteration over x-coordinate
N = self.N
f = self.f
j = 0
d = []
thethastar = np.full((N + 1, N + 1), 0, dtype='f')
for i in range(0, N - 1):
d.append(2 * thetha[i][j + 1] + f * thetha[i][j])
d.append(2 * thetha[N - 1][j + 1] + f * thetha[N - 1][j] + thetha[N][j])
u = self.formMatrix(d, N)
for i in range(0, N):
thethastar[i][j] = u[i]
for j in range(1, N):
d = []
for i in range(0, N - 1):
d.append(thetha[i][j - 1] + f * thetha[i][j] + thetha[i][j + 1])
d.append(thetha[N - 1][j - 1] + f * thetha[N - 1][j] + thetha[N][j + 1] + thetha[N][j])
u = self.formMatrix(d, N)
for i in range(0, N):
thethastar[i][j] = u[i]
return thethastar

def Halfstepj(self, thetha): # Implicit iteration over y-coordinate
N = self.N
f = self.f
i = 0
d = []
thethastar = np.full((N + 1, N + 1), 0, dtype='f')
for j in range(0, N - 1):
d.append(2 * thetha[i + 1][j] + f * thetha[i][j])
d.append(2 * thetha[i + 1][N - 1] + f * thetha[i][N - 1] + thetha[i][N])
u = self.formMatrix(d, N)
for j in range(0, N):
thethastar[i][j] = u[j]
for i in range(1, N):
d = []
for j in range(0, N - 1):
d.append(thetha[i - 1][j] + f * thetha[i][j] + thetha[i + 1][j])
d.append(thetha[i - 1][N - 1] + f * thetha[i][N - 1] + thetha[i + 1][N] + thetha[i][N])
u = self.formMatrix(d, N)
for j in range(0, N):
thethastar[i][j] = u[j]
return thethastar

def extendsquare(self, A, N): # Extended the matrix in all direction(Symmetry)
box = np.full((2 * N - 1, 2 * N - 1), 0, dtype='f')
for i in range(0, N):
for j in range(0, N):
box[N - 1 - i][N - 1 - j] = A[i][j]
box[N - 1 - i][N - 1 + j] = A[i][j]
box[N - 1 + i][N - 1 - j] = A[i][j]
box[N - 1 + i][N - 1 + j] = A[i][j]
return box

def solve(self): # Simulates the diffusion using ADI method
N = self.N
fig = plt.figure()
ax = fig.add_subplot(111)
thetha = np.full((N + 1, N + 1), 0, dtype='f') # Dimensionless temperature
ims = [] # stores thetha at different timesteps later used to visualise
im = imshow(self.extendsquare(thetha, N + 1), animated=True)
ims.append([im])
self.dirichelet(thetha, N)
for t in range(self.nit): # time marching
thethastar = self.Halfstepi(thetha) # updates thetha after half time step
self.updatevalue(thetha, thethastar, N)
thethastar = self.Halfstepj(thetha)
self.updatevalue(thetha, thethastar, N) # updates thetha after second half time step
box = self.extendsquare(thetha, N + 1)
temp = int(thetha[0][0] * (
self.T0 - self.Tin) + self.Tin) # next three lines are for the showing timestep and temperature
time = plt.text(0.1, 0.1, "Timestep: " + str(t), horizontalalignment='left', verticalalignment='top',
transform=ax.transAxes)
temp = ax.text(0.98, 0.95, "Core Temperature: " + str(temp) + "K", horizontalalignment='right',
verticalalignment='top', transform=ax.transAxes)
im = imshow(box, vmin=0, vmax=1, animated=True)
if t % 2 == 0: # only visualising at every other time step
ims.append([im, time, temp])
anim = ani.ArtistAnimation(fig, ims, blit=True, interval=600, repeat_delay=10)
show()