Pressure dither in venting analyses

Venting analyses simulate the time-dependent flow of air or another gas from one compartment to another, or to an ambient profile. The flow through the vent connecting the compartments is assumed to be one-dimensional, quasi-steady, and isentropic with an empirical discharge coefficient included to account for irreversible flow losses. When a venting analysis is performed numerically, an upper limit on the accuracy exists due to the effects of the numerical integration method. Because this manifests itself in a first-order method by a rapid oscillation about the true answer, this phenomenon is referred to as pressure dither. This paper explores the origin of the phenomenon and gives simple formulae for predicting when it will occur and the greatest achievable accuracy for a given time step.