Numerical simulations for non conservative hyperbolic system. Application to transient two-phase flow with cavitation phenomenon

A numerical method for simulating transient flows of gas-liquid mixtures is proposed. The mathematical model, established for a suspension of gas bubbles in liquid, includes an equation taking into account the relative velocity between the gas and liquid. A numerical technique based on the MacCormack scheme combined with the method of characteristics is presented. Theoretical results for transients initiated by a rapid closing valves are compared with measurements. A good agreement is found particularly for large values of initial dissolved gas concentration