I have a specific question about fluid analysis that is bugging me. I am no expert in this field but very interested in it. Lets's say we want to model a flow where air expands out of an air reservoir across a valve into a cylinder and applies a pressure force on an airtight piston, which moves, allowing the air to further expand. Assume we know the inertial and frictional forces which resist the movement of the piston as well as the initial pressure in the reservoir before the opening of the valve. Also assume that the valve opens instantaneously. We would like to obtain (by numerical analysis) the functions of the piston's velocity as well as the pressure just behind with respect to time. How is such a moving (dynamic) boundary, as it shows up at the piston, usually treated? At the same time, the solid boundary at the parts of the valve, which are fixed in space, should also be included. Does anyone know how such problems could be solved using CFD methods or some other method?