  We consider a mathematical model for the gas flow through a one-way valve and
focus on two issues. First, we propose a way to eliminate the chattering (the
fast switch on and off of the valve) by slightly modifying the design of the
valve. This mathematically amounts to the construction of a coupling Riemann
solver with a suitable stability property, namely, coherence. We provide a
numerical comparison of the behavior of the two valves. Second, we analyze,
both analytically and numerically, for several significative situations, the
maximization of the flow through the modified valve according to a control
parameter of the valve and time.
