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

"""
***********************************************************************************
tutorial_dealii_2.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 example a simple transient heat convection-diffusion equation is solved.

.. code-block:: none

dT/dt - kappa/(rho*cp)*nabla^2(T) + nabla.(uT) = g(T) in Omega

The fluid flows from the left side to the right with constant velocity of 0.01 m/s.
The inlet temperature for 0.2 <= y <= 0.3 is iven by the following expression:

.. code-block:: none

T_left = T_base + T_offset*|sin(pi*t/25)| on dOmega

creating a bubble-like regions of higher temperature that flow towards the right end
and slowly diffuse into the bulk flow of the fluid due to the heat conduction.

The mesh is rectangular with the refined elements close to the left/right ends:

.. image:: _static/rect(1.5,0.5)-100x50.png
:width: 500 px

The temperature plot at t = 500s:

.. image:: _static/tutorial_dealii_2-results.png
:width: 600 px
"""

import os, sys, numpy, json, 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

# Nota bene:
#   This function is derived from Function_2D class and returns "double" value/gradient
class VelocityFunction_2D(Function_2D):
def __init__(self, velocity, direction, n_components = 1):
"""
Arguments:
velocity  - float, velocity magnitude
direction - Tensor<1,dim>, unit vector
"""
Function_2D.__init__(self, n_components)
self.m_velocity = Tensor_1_2D()
self.m_velocity[0] = velocity * direction[0]
self.m_velocity[1] = velocity * direction[1]

def gradient(self, point, component = 0):
return self.m_velocity

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

def __init__(self, ymin, ymax, T_base, T_offset, n_components = 1):
"""
The function creates bubble-like regions of fluid with a higher temperature.
Arguments:
ymin     - float
ymax     - float
T_base   - float
T_offset - float
Return value:
T_base + T_offset * |sin(t/25)|
"""

self.ymin = ymin
self.ymax = ymax

def value(self, point, component = 0):
if point.y > self.ymin and point.y < self.ymax:
return self.T_base + self.T_offset*numpy.fabs(numpy.sin(numpy.pi*Time()/25))
else:
return self.T_base

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)

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]))

meshes_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'meshes')
mesh_file  = os.path.join(meshes_dir, 'rect(1.5,0.5)-100x50.msh')

# 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('HeatConvection', self, 'Transient heat convection', self.fe_system)

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

# Thermo-physical properties of the liquid (water).
# The specific heat conductivity is normally 0.6 W/mK,
# however, here we used much larger value to amplify the effect of conduction
rho   = 1000.0  # kg/m**3
cp    = 4181.0  # J/(kg*K)
kappa =  100.0  # W/(m*K)
# Thermal diffusivity (m**2/s)
alpha = kappa/(rho * cp)

# Velocity is in the positive x-axis direction
velocity  = 0.01   # The velocity magnitude, m/s
direction = (1, 0) # The velocity direction (unit vector)

# The dimensions of the 2D domain is a rectangle: x=[0,2] and y=[0,0.5]
ymin = 0.2
ymax = 0.3
T_base   = 300 # Base temperature, K
T_offset = 50  # Offset temperature, K

# Boundary IDs
left_edge   = 0
top_edge    = 1
right_edge  = 2
bottom_edge = 3

dirichletBC = {}
dirichletBC[left_edge]  = [
('T',  TemperatureSource_2D(ymin, ymax, T_base, T_offset, self.n_components)),
]

# Function<dim> wrapper
# Function<dim>::value wrappers

# FE weak form terms
accumulation = (phi_2D('T', fe_i, fe_q) * phi_2D('T', fe_j, fe_q)) * JxW_2D(fe_q)
diffusion    = (dphi_2D('T', fe_i, fe_q) * dphi_2D('T', fe_j, fe_q)) * alpha * JxW_2D(fe_q)
convection   = phi_2D('T', fe_i, fe_q) * (u_grad * dphi_2D('T', fe_j, fe_q)) * JxW_2D(fe_q)
source       = phi_2D('T', fe_i, fe_q) * 0.0 * JxW_2D(fe_q)

weakForm = dealiiFiniteElementWeakForm_2D(Aij = diffusion + convection,
Mij = accumulation,
Fi  = source,
functionsDirichletBC = dirichletBC)

print('Transient heat convection equations:')
print('    Aij = %s' % str(weakForm.Aij))
print('    Mij = %s' % str(weakForm.Mij))
print('    Fi  = %s' % str(weakForm.Fi))
print('    boundaryFaceAij = %s' % str([item for item in weakForm.boundaryFaceAij]))
print('    boundaryFaceFi  = %s' % str([item for item in weakForm.boundaryFaceFi]))
print('    innerCellFaceAij = %s' % str(weakForm.innerCellFaceAij))
print('    innerCellFaceFi  = %s' % str(weakForm.innerCellFaceFi))
print('    surfaceIntegrals  = %s' % str([item for item in weakForm.surfaceIntegrals]))

# 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_2")
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', 300.0)

# Use daeSimulator class
def guiRun(app):
datareporter = daeDelegateDataReporter()
simulation   = simTutorial()
lasolver = pySuperLU.daeCreateSuperLUSolver()

simName = simulation.m.Name + strftime(" [%d.%m.%Y %H:%M:%S]", localtime())
results_folder = tempfile.mkdtemp(suffix = '-results', prefix = 'tutorial_deal_II_2-')

# Create two data reporters:
# 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()
if not tcpipDataReporter.Connect("", simName):
sys.exit()

daeQtMessage("deal.II", "The simulation results will be located in: %s" % results_folder)

simulation.m.SetReportingOn(True)
simulation.ReportingInterval = 2
simulation.TimeHorizon       = 200
simulator  = daeSimulator(app, simulation=simulation, datareporter = datareporter, lasolver=lasolver)
simulator.exec_()

# Setup everything manually and run in a console
def consoleRun():
# Create Log, Solver, DataReporter and Simulation object
log          = daePythonStdOutLog()
daesolver    = daeIDAS()
datareporter = daeDelegateDataReporter()
simulation   = simTutorial()

lasolver = pySuperLU.daeCreateSuperLUSolver()
daesolver.SetLASolver(lasolver)

simName = simulation.m.Name + strftime(" [%d.%m.%Y %H:%M:%S]", localtime())
results_folder = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'tutorial_deal_II_2-results')

# Create two data reporters:
# 1. DealII
feDataReporter = simulation.m.fe_system.CreateDataReporter()
if not feDataReporter.Connect(results_folder, simName):
sys.exit()

# 2. TCP/IP
tcpipDataReporter = daeTCPIPDataReporter()
if not tcpipDataReporter.Connect("", simName):
sys.exit()

# Enable reporting of all variables
simulation.m.SetReportingOn(True)

# Set the time horizon and the reporting interval
simulation.ReportingInterval = 2
simulation.TimeHorizon = 200

# Initialize the simulation
simulation.Initialize(daesolver, datareporter, log)

# Save the model report and the runtime model report
simulation.m.fe_model.SaveModelReport(simulation.m.Name + ".xml")
#simulation.m.fe_model.SaveRuntimeModelReport(simulation.m.Name + "-rt.xml")

# Solve at time=0 (initialization)
simulation.SolveInitial()

# Run
simulation.Run()
simulation.Finalize()

if __name__ == "__main__":
if len(sys.argv) > 1 and (sys.argv[1] == 'console'):
consoleRun()
else:
app = daeCreateQtApplication(sys.argv)
guiRun(app)
```