```#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
***********************************************************************************
tutorial_dealii_4.py
DAE Tools: pyDAE module, www.daetools.com
***********************************************************************************
DAE Tools is free software; you can redistribute it and/or modify it under the
Foundation. DAE Tools is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with the
DAE Tools software; if not, see <http://www.gnu.org/licenses/>.
************************************************************************************
"""
__doc__ = """
In this tutorial the transient heat conduction problem is solved using
the finite element method:

.. code-block:: none

dT/dt - kappa * nabla^2(Τ) = g in Omega

The mesh is a pipe submerged into water receiving the heat of the sun at the
45 degrees from the top-left direction, the heat from the suroundings and
having the constant temperature of the inner tube.
The boundary conditions are thus:

- [at boundary ID=0] Sun shine at 45 degrees, gradient heat flux = 2 kW/m**2 in direction n = (1,-1)
- [at boundary ID=1] Outer surface where y <= -0.5, constant flux of 2 kW/m**2
- [at boundary ID=2] Inner tube: constant temperature of 300 K

The pipe mesh is given below:

.. image:: _static/pipe.png
:width: 300 px

The temperature plot at t = 3600s:

.. image:: _static/tutorial_dealii_4-results.png
:height: 400 px

Animation:

.. image:: _static/tutorial_dealii_4-animation.gif
:height: 400 px
"""

import os, sys, numpy, json, math, tempfile
from time import localtime, strftime
from daetools.pyDAE import *
from daetools.solvers.deal_II import *
from daetools.solvers.superlu import pySuperLU

# Standard variable types are defined in variable_types.py
from pyUnits import m, kg, s, K, Pa, mol, J, W

# Neumann BC use either value() or gradient() functions.
# Dirichlet BC use vector_value() with n_component = multiplicity of the equation.
# Other functions use just the value().
#
# Nota bene:
#   This function is derived from Function_2D class and returns "double" value/gradient
def __init__(self, gradient, direction, n_components = 1):
"""
Arguments:
direction - Tensor<1,dim>, unit vector
"""
Function_2D.__init__(self, n_components)

def gradient(self, point, component = 0):
if point.x < 0 and point.y > 0:
else:
return Tensor_1_2D()

return [self.gradient(point, c) for c in range(self.n_components)]

# Nota bene:
#   This function is derived from adoubleFunction_2D class and returns "adouble" value
#   In this case, it is a function of daetools parameters/variables
def __init__(self, gradient, n_components = 1):
"""
Arguments:
"""

def value(self, point, component = 0):
if point.y < -0.5:
else:

def vector_value(self, point):
return [self.value(point, c) for c in range(self.n_components)]

class modTutorial(daeModel):
def __init__(self, Name, Parent = None, Description = ""):
daeModel.__init__(self, Name, Parent, Description)

self.Q0_total = daeVariable("Q0_total", no_t, self, "Total heat passing through the boundary with id=0")
self.Q1_total = daeVariable("Q1_total", no_t, self, "Total heat passing through the boundary with id=1")
self.Q2_total = daeVariable("Q2_total", no_t, self, "Total heat passing through the boundary with id=2")

meshes_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'meshes')
mesh_file  = os.path.join(meshes_dir, 'pipe.msh')

dofs = [dealiiFiniteElementDOF_2D(name='T',
description='Temperature',
fe = FE_Q_2D(1),
multiplicity=1)]
self.n_components = int(numpy.sum([dof.Multiplicity for dof in dofs]))

# Store the object so it does not go out of scope while still in use by daetools
self.fe_system = dealiiFiniteElementSystem_2D(meshFilename    = mesh_file,     # path to mesh
dofs            = dofs)          # degrees of freedom

self.fe_model = daeFiniteElementModel('HeatConduction', self, 'Transient heat conduction through a pipe wall with an external heat flux', self.fe_system)

def DeclareEquations(self):
daeModel.DeclareEquations(self)

# Thermo-physical properties of copper.
rho   = 8960.0  # kg/m**3
cp    =  385.0  # J/(kg*K)
kappa =  401.0  # W/(m*K)

# Thermal diffusivity (m**2/s)
alpha        = kappa / (rho*cp)   # m**2/s

flux_above   = 2.0E3/(rho*cp) # (W/m**2)/((kg/m**3) * (J/(kg*K))) =
flux_beneath = 5.0E3/(rho*cp) # (W/m**2)/((kg/m**3) * (J/(kg*K))) =

print('Thermal diffusivity = %f' % alpha)
print('Beneath source flux = %f' % flux_beneath)
print('Above source flux = %f x (1,-1)' % flux_above)

# Create some auxiliary objects for readability
phi_i  =  phi_2D('T', fe_i, fe_q)
phi_j  =  phi_2D('T', fe_j, fe_q)
dphi_i = dphi_2D('T', fe_i, fe_q)
dphi_j = dphi_2D('T', fe_j, fe_q)
dof_T  = dof_2D('T', fe_i)
normal = normal_2D(fe_q)
xyz    = xyz_2D(fe_q)
JxW    = JxW_2D(fe_q)

# deal.II Function<dim,Number> wrappers.
self.fun_Diffusivity = ConstantFunction_2D(alpha)
self.fun_Generation  = ConstantFunction_2D(0.0)
# Gradient flux at boundary id=0 (Sun)
self.fun_Flux_a = GradientFunction_2D(flux_above, direction = (-1, 1))
# Flux as a function of daetools variables at boundary id=1 (outer tube where y < -0.5)

# Nota bene:
#   For the Dirichlet BCs only the adouble versions of Function<dim> class can be used.
#   The values allowed include constants and expressions on daeVariable/daeParameter objects.
dirichletBC    = {}
dirichletBC[2] = [ ('T', adoubleConstantFunction_2D( adouble(300) )) ] # at boundary id=2 (inner tube)

surfaceIntegrals = {}
surfaceIntegrals[0] = [(self.Q0_total(), (-kappa * (dphi_i * normal) * JxW) * dof_T)]
surfaceIntegrals[1] = [(self.Q1_total(), (-kappa * (dphi_i * normal) * JxW) * dof_T)]
surfaceIntegrals[2] = [(self.Q2_total(), (-kappa * (dphi_i * normal) * JxW) * dof_T)]

D      = function_value_2D        ('Diffusivity', self.fun_Diffusivity, xyz)
G      = function_value_2D        ('Generation',  self.fun_Generation,  xyz)
Flux_a = function_gradient_2D     ('Flux_a',      self.fun_Flux_a,      xyz)

# FE weak form terms
accumulation = (phi_i * phi_j) * JxW
diffusion    = (dphi_i * dphi_j) * D * JxW
source       = phi_i * G * JxW
faceFluxes   = {
0: phi_i * (Flux_a * normal) * JxW,
1: phi_i * Flux_b * JxW
}

cell_Aij = diffusion
cell_Mij = accumulation
cell_Fi  = source

weakForm = dealiiFiniteElementWeakForm_2D(Aij = cell_Aij,
Mij = cell_Mij,
Fi  = cell_Fi,
boundaryFaceFi  = faceFluxes,
functionsDirichletBC = dirichletBC,
surfaceIntegrals = surfaceIntegrals)

print('Transient heat conduction equation:')
print('    Aij = %s' % str(cell_Aij))
print('    Mij = %s' % str(cell_Mij))
print('    Fi  = %s' % str(cell_Fi))

# Setting the weak form of the FE system will declare a set of equations:
# [Mij]{dx/dt} + [Aij]{x} = {Fi} and boundary integral equations
self.fe_system.WeakForm = weakForm

class simTutorial(daeSimulation):
def __init__(self):
daeSimulation.__init__(self)
self.m = modTutorial("tutorial_dealii_4")
self.m.Description = __doc__
self.m.fe_model.Description = __doc__

def SetUpParametersAndDomains(self):
pass

def SetUpVariables(self):
# setFEInitialConditions(daeFiniteElementModel, dealiiFiniteElementSystem_xD, str, float|callable)
setFEInitialConditions(self.m.fe_model, self.m.fe_system, 'T', 293)

def run(**kwargs):
guiRun = kwargs.get('guiRun', False)

simulation = simTutorial()

# Create SuperLU LA solver
lasolver = pySuperLU.daeCreateSuperLUSolver()

# Create and setup two data reporters:
datareporter = daeDelegateDataReporter()
simName = simulation.m.Name + strftime(" [%d.%m.%Y %H:%M:%S]", localtime())
if guiRun:
results_folder = tempfile.mkdtemp(suffix = '-results', prefix = 'tutorial_deal_II_4-')
daeQtMessage("deal.II", "The simulation results will be located in: %s" % results_folder)
else:
results_folder = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'tutorial_deal_II_4-results')
print("The simulation results will be located in: %s" % results_folder)

# 1. deal.II (exports only FE DOFs in .vtk format to the specified directory)
feDataReporter = simulation.m.fe_system.CreateDataReporter()
if not feDataReporter.Connect(results_folder, simName):
sys.exit()

# 2. TCP/IP
tcpipDataReporter = daeTCPIPDataReporter()