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Example 1: Porous Material
==========================
An OpenBTE simulation is specified by a combination of a material, geometry and solver. We begin with creating a material. To this end, we load previously computed first-principled calculations on Si at room temperature
.. code-block:: python
from openbte import load_rta
rta_data = load_rta('Si_rta')
Next step is to perform MFP interpolation
.. code-block:: python
from openbte import RTA2DSym
mat = RTA2DSym(rta_data)
The ``RTA2DSym`` model is for simulation domains which have translational symmetry along the z axis. To create a geometry, we instantiate an object of the class ``Geometry``
.. code-block:: python
from openbte import Geometry
G = Geometry(0.1)
where :math:`0.1` is the carhacteristic size (in nm) of the mesh. In this example, we create a porous material with porosity :math:`0.2` and rectangular aligned pores. Given the periodicity of the system, we simulate only a unit-cell to which we apply periodic boundary conditions. To define the unit-cell, we use the ``add_shape`` method
.. code-block:: python
from openbte import rectangle
L = 10 #nm
G.add_shape(rectangle(area = L*L))
To add the hole in the middle, we use the ``add_hole`` method
.. code-block:: python
porosity = 0.2
area = porosity*L*L
G.add_hole(rectangle(area = area,x=0,y=0))
To apply boundary conditions, we need to assign a name to sides and refer to them in the solver section. Sides are selected with ``selector``. In this case, we assign all internal sides the name ``Boundary``
.. code-block:: python
G.set_boundary_region(selector = 'inner',region = 'Boundary')
To apply periodic boundary conditions along both axes, we use the ``set_periodicity`` method
.. code-block:: python
G.set_periodicity(direction = 'x',region = 'Periodic_x')
G.set_periodicity(direction = 'y',region = 'Periodic_y')
At this point, we are ready to save the mesh on disk
.. code-block:: python
G.write_geo()
If everything went smoothly, you should see ``mesh.geo`` in your current directory. You can open them with GMSH_ to check that the geometry has been created correctly. To create a meshed geometrym we use the function ``get_mesh()``
.. code-block:: python
from openbte import get_mesh
mesh = get_mesh()
Before setting up the solvers, we need to specify boundary conditions and perturbation. In this case, we apply a difference of temperature of :math:`\Delta T_{\mathrm{ext}} = 1` K along x
.. code-block:: python
from openbte.objects import BoundaryConditions
boundary_conditions = BoundaryConditions(periodic={'Periodic_x': 1,'Periodic_y':0},diffuse='Boundary')
Note that we also specifies diffuse boundary conditions along the region ``Boundary``. In this example, we are interested in the effective thermal conductivity along x
.. code-block:: python
from openbte.objects import EffectiveThermalConductivity
effective_kappa = EffectiveThermalConductivity(normalization=-1,contact='Periodic_x')
where ``normalization`` (:math:`\alpha`) is used in the calculation of the effective thermal conductivity :math:`\kappa_{\mathrm{eff}} = \alpha\int_{-L/2}^{L/2}\mathbf{J}(L/2,y)\cdot \mathbf{\hat{n}}dy`. For rectangular domain, :math:`\alpha =-L_x/L_y/\Delta T_{\mathrm{ext}}`.
To run BTE calculations, we first solve standard heat conduction
.. code-block:: python
from openbte import Fourier
fourier = Fourier(mesh,mat.kappa,boundary_conditions,\
effective_thermal_conductivity=effective_kappa)
Finally, using ``fourier`` as first guess, we solve the BTE
.. code-block:: python
from openbte import BTE_RTA
bte = BTE_RTA(mesh,mat,boundary_conditions,fourier=fourier,\
effective_thermal_conductivity=effective_kappa)
Before plotting the results, we group together Fourier and BTE results
.. code-block:: python
from openbte.objects import OpenBTEResults
results = OpenBTEResults(mesh=mesh,material = mat,solvers=[fourier,bte])
Lastly, the temperature and heat flux maps can be obtained with
.. code-block:: python
results.show()
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`GMSH `_