In general, one cannot prescribe both the pressure at and the flow through a node at the same time. If a pressure is prescribed, using an ideal pressure source, the flow through the source is determined by the downstream flow resistance. If a flow is prescribed, using an ideal flow source, the pressure at the source outlet is determined by the pressure needed to generate such flow through the downstream resistances.
In this model, the pressure at the outlets of the two sources, and the inlet of the check valve, is prescribed by the pressure source. The check valve will let through a certain amount of flow calculated from its parametrization (e.g. opening pressure & orifice area). This flow may be greater or less than the prescribed flow at the flow source. The deficit or surplus will flow through the pressure source.
If you have both the reference flow and pressure, the proper way to use such information is to parametrize the check valve so that both can be satisfied when using either a pressure source or a flow source.
