defining periodical changing boundary conditions

edodo

>
> I want to know how to define a function for the periodical changing
> boundary conditions. For my case, the inlet concentration of a tube
> reactor changes with time in a cycle with concentration of 1 for 60
> seconds and concentration of 0 for 10 seconds. This cycle repeats
> until reaching my defined end time. Need it urgently.  Thanks.

edodo

Hi,

At the risk offending all users again by plugging my book, I did
something similar with Jordan MacInnes in Chapter 9 of Process
Modelling and Simulation with Finite Element Methods...

We wanted a "square wave" input to each of two voltages controlling
an electrokinetic, microfluidic flow in a Y-junction.  Each leg of
the Y has to alternate between "idle" and "on" voltages so that flow
switches downstream with source from the other leg.  You might think
that this can be easily done
by altering your Dirichlet boundary conditions to include sinusoids
in time with the appropriate logical operator to turn it into a
square wave (sine > 0 for instance) and out-of-phase behavior for
each leg.  I tried this, and it is not straightforward because of the
elliptic nature of my PDE system and because the FEMLAB
implementation involves weak boundary constraints.  My system
was "stiff" as it involves an infinitely fast time scale, so I tried
approximating the square wave with a few terms of its Fourier series
to smooth it, and then I simply did the periodic switching in a
Matlab driver file that calls the Femlab subroutines with the
appropriate changes to the contants and the solution in the last time
interval as the initial condition.  If your system is not "stiff", I
think the weak boundary constraint that is time varying ought to work
for you.

Regards,
Will Zimmerman