Narrow gaps are present in rotating and reciprocating machinery such as turbines, compressors, pistons, and gear pumps. These narrow gaps are often essential for the operation of the machinery, as leakage of the working fluid through the narrow gap provides lubrication between the moving parts, and these narrow gaps frequently are moving. Narrow gaps can also be used in the computational fluid model although not seen in the physical problem. This occurs in models with solid-to-solid contact. For example, consider the reed valve shown in Figure 1. Reed valves are a type of check valve that restrict flow to a single direction, opening and closing under changing pressure on each face. When the reed valve is open, fluid flows from the inlet port to the top chamber. When the reed valve is closed, solid-to-solid contact between the reed valve and the inlet port seat prevents flow. Ā (a)Reed valve is open. Fluid flows from the inlet port to the top chamber. (b) Reed valve is closed. There is no fluid flow. Figure 1Ā Ā Fluid flow through a reed valve In the analysis of a reed valve, see here for an example of aĀ piston with a suction reed valve, fluid elements must