modellib/py_src/temperature.py

# $Id$

from escript.escript import *
from escript.modelframe import Model,IterationDivergenceError
from escript.linearPDEs import AdvectivePDE,LinearPDE
import numarray


class TemperatureAdvection(Model):
       """

         The conservation of internal heat energy is given by

         \f[
             \rho c_p ( T_{,t}+v_{j}T_{,j} )-(\kappa T_{,i})_{,i}=Q,
         \f]
         \f[
                 n_i\kappa T_{,i}=0
         \f]

          it is assummed that \f[ \rho c_p \f] is constant in time.

          solved by Taylor Galerkin method

       """
       def __init__(self,debug=False):
           Model.__init__(self,debug=debug)
           self.declareParameter(domain=None, \
                                 temperature=1., \
                                 velocity=numarray.zeros([3]),
                                 density=1., \
                                 heat_capacity=1., \
                                 thermal_permabilty=1., \
                                 # reference_temperature=0., \
                                 # radiation_coefficient=0., \
                                 thermal_source=0., \
                                 fixed_temperature=0.,
                                 location_fixed_temperature=Data(),
                                 safety_factor=0.1)

       def doInitialization(self):
           self.__pde=LinearPDE(self.domain)
           self.__pde.setSymmetryOn()
           # self.__pde.setReducedOrderOn()
           # self.__pde.setLumpingOn()
           self.__pde.setValue(D=self.heat_capacity*self.density)

       def getSafeTimeStepSize(self,dt):
           """returns new step size"""
           h=self.domain.getSize()
           return self.safety_factor*inf(h**2/(h*abs(self.heat_capacity*self.density)*length(self.velocity)+self.thermal_permabilty))

       def G(self,T,alpha):
           """tangential operator for taylor galerikin"""
           g=grad(T)
           self.__pde.setValue(X=-self.thermal_permabilty*g, \
                               Y=self.thermal_source-self.__rhocp*inner(self.velocity,g), \
                               r=(self.__fixed_T-self.temperature)*alpha,\
                               q=self.location_fixed_temperature)
           return self.__pde.getSolution()
           

       def doStepPostprocessing(self,dt):
           """perform taylor galerkin step"""
           T=self.temperature
       self.__rhocp=self.heat_capacity*self.density
           self.__fixed_T=self.fixed_temperature
           self.temperature=dt*self.G(dt/2*self.G(T,1./dt)+T,1./dt)+T
           self.trace("Temperature range is %e %e"%(inf(self.temperature),sup(self.temperature)))
1	# $Id$
2
3	from escript.escript import *
4	from escript.modelframe import Model,IterationDivergenceError
5	from escript.linearPDEs import AdvectivePDE,LinearPDE
6	import numarray
7
8
9	class TemperatureAdvection(Model):
10	"""
11
12	The conservation of internal heat energy is given by
13
14	\f[
15	\rho c_p ( T_{,t}+v_{j}T_{,j} )-(\kappa T_{,i})_{,i}=Q,
16	\f]
17	\f[
18	n_i\kappa T_{,i}=0
19	\f]
20
21	it is assummed that \f[ \rho c_p \f] is constant in time.
22
23	solved by Taylor Galerkin method
24
25	"""
26	def __init__(self,debug=False):
27	Model.__init__(self,debug=debug)
28	self.declareParameter(domain=None, \
29	temperature=1., \
30	velocity=numarray.zeros([3]),
31	density=1., \
32	heat_capacity=1., \
33	thermal_permabilty=1., \
34	# reference_temperature=0., \
35	# radiation_coefficient=0., \
36	thermal_source=0., \
37	fixed_temperature=0.,
38	location_fixed_temperature=Data(),
39	safety_factor=0.1)
40
41	def doInitialization(self):
42	self.__pde=LinearPDE(self.domain)
43	self.__pde.setSymmetryOn()
44	# self.__pde.setReducedOrderOn()
45	# self.__pde.setLumpingOn()
46	self.__pde.setValue(D=self.heat_capacity*self.density)
47
48	def getSafeTimeStepSize(self,dt):
49	"""returns new step size"""
50	h=self.domain.getSize()
51	return self.safety_factorinf(h2/(habs(self.heat_capacityself.density)length(self.velocity)+self.thermal_permabilty))
52
53	def G(self,T,alpha):
54	"""tangential operator for taylor galerikin"""
55	g=grad(T)
56	self.__pde.setValue(X=-self.thermal_permabilty*g, \
57	Y=self.thermal_source-self.__rhocp*inner(self.velocity,g), \
58	r=(self.__fixed_T-self.temperature)*alpha,\
59	q=self.location_fixed_temperature)
60	return self.__pde.getSolution()
61
62
63	def doStepPostprocessing(self,dt):
64	"""perform taylor galerkin step"""
65	T=self.temperature
66	self.__rhocp=self.heat_capacity*self.density
67	self.__fixed_T=self.fixed_temperature
68	self.temperature=dtself.G(dt/2self.G(T,1./dt)+T,1./dt)+T
69	self.trace("Temperature range is %e %e"%(inf(self.temperature),sup(self.temperature)))
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