An efficient integration algorithm for a class of discontinuous dynamical systems in sliding motion

An ideal gas-liquid discontinuous dynamical system at sliding motion is studied. The discontinuity sticks while described by the gas model, and hence, integrated over a fixed time step. A discontinuity algorithm detects the exact time duration of applicability of the liquid model. The ratio of time of applicability of the liquid model to that of the gas model is a smooth graph and it is in agreement with the analytical results. In addition, this is shown to be an efficient way to numerically solve the system while in sliding motion.