The concept of correctness of the numerical solution of a gas-liquid system with persistent discontinuity sticking in the gas model is proposed. An algorithm that handles discontinuity while in the liquid model alone is shown to be correct. This technique IS pplied to the gas-liquid system with linear hydraulics and compared with the analytical solution. For a system with square-root hydraulics, the results of thIS pproach are compared with those obtained from the numerical solution of equivalent dynamics. The proposed technique is one to two orders of magnitude more efficient than a previously reported, and a less accurate, method.