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How I can shrink or expand my simulation box?

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Hi all,
I have a simulation box to simulate a special form of the diffusion problem (I have my own PDE). I have only one field say density "ro" which varies during the simulation in the box. I want to have constant amount of mass in the box all the time or integral of ro over the volume constant. One way to do so is to change the size of the box in one direction during the simulation according to the constant mass constraint which is the way I want to do physically.

My questions are:
1) How I can add an integral constraint to my equations? and
2) How I can change the simulation size according to 1?
or the two steps are only one!!?

Any help or suggestion is appreciated much.

Abe

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