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integrals.py
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integrals.py
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'''
Author: Andy Wang
Description: Various nested integrals for use in other modules
Important Functions
ReferenceVolumeIntegral: int int int (f) dV
ReferenceFaceIntegral: int int (f).dS
where (v1).(v2) is the dot product of two vectors (v1) and (v2)
'''
from sympy import integrate
from globalVars import dimension, X, Y, Z
def ReferenceVolumeIntegral(f):
if dimension == 2:
v = integrate(f, (Y,0,1-X))
v = integrate(v, (X,0,1))
elif dimension == 3:
v = integrate(f, (Z,0,1-X-Y))
v = integrate(v, (Y,0,1-X))
v = integrate(v, (X,0,1))
return float(v)
def ReferenceFaceIntegral(f, i):
if dimension == 2:
if i == 0:
v = f.subs(Y, 0)
v = integrate(v, (X,0,1))
elif i == 1:
v = f.subs(X, 0)
v = integrate(v, (Y,0,1))
elif i == 2:
v = f.subs(Y, 1-X)
v = integrate(v, (X,0,1))
else:
raise Exception("Please enter a value of 'i' in [0,2]")
elif dimension == 3:
if i == 0:
v = f.subs(Z, 0)
v = integrate(v, (Y,0,1-X))
v = integrate(v, (X,0,1))
elif i == 1:
v = f.subs(Y, 0)
v = integrate(v, (Z,0,1-X))
v = integrate(v, (Z,))
elif i == 2:
v = f.subs(X, 0)
v = integrate(v, (Z,0,1-Y))
v = integrate(v, (Y,0,1))
elif i == 3:
v = f.subs(Z, 1-X-Y)
v = integrate(v, (Y,0,1-X))
v = integrate(v, (X,0,1))
else:
raise Exception("Please enter a value of 'i' in [0,3]")
return float(v)