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Many computational methods have been suggested for the solution of this theoretical situation, such as Riemann variables, Lax-Wendroff and other finite difference procedures. The basic approach adopted here is to re-examine the fundamental theory of pressure wave motion and adapt it to a mesh method interpolation procedure. At the same time the boundary conditions for inflow and outflow, such as the filling and emptying of engine cylinders, has been resolved for the generality of gas properties and in terms of the unsteady gas flow which controls those processes. The same generality of gas property and composition is traced throughout the pipe system. This change of gas property is very significant in two-stroke engines where the exhaust blowdown is followed by short-circuited scavenge air.