Tuesday, July 2, 2013

Python Software Foundation - SfePy : GSoC 2013 : Week 2

Hi Pythonistas,

After developing more understanding of SfePy I moved towards implementation.
The first phase of my project involved implementation of convective-diffusive equations.

So with the help of my mentor R (Robert. He is awesome!), energy equations were implemented.

The sample problem taken was:

Steady Axial convection and diffusion in slug flow with velocity :math:`U _0`
in an insulated pipe.
It is subjected to specified temperature at the entry and exit lengths -
:math:`T _0 for x \leqslant 0`
:math:`T _1 for x \geqslant L`
:math:`\alpha \frac {\partial T}{\partial n} = 0 on the lateral surface of the pipe`
Find :math:`T` such that:
.. math::
        \int_{\Omega} c \nabla v \cdot \nabla T =
        - \int_{\Omega_L} (\vec{u} \cdot \nabla T) v

Now the results were pretty interesting :

The results were in accordance with the Peclet number graph which predicts the Temperature distribution in a convective-diffusive case. 

We have realised that a robust Navier-Stokes solver is necessary for the project compared to the present solver so our next task is to get that in place and then move ahead with the coupling of the two equations.


Up Next: Navier-Strokes Eq. Solver

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