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The check valve problem to be considered is shown schematically in Figure 13.1. A 2D axisymmetric valve geometry is used, consisting of a mass flow inlet on the left, and a pressure outlet on the right, driving the motion of a valve. In this case, the transient motion of the valve due to spring force, gravity, and hydrodynamic force is studied. Note, however, that the valve in this case is not completely closed. Instead, for the sake of simplicity, a small gap remains between the valve and the valve seat (since dynamic mesh problems require that at least one layer remains in order to maintain the topology).