Coherence and flow-maximization of a one-way valve

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