Numerical analysis of pressure transients in bubbly two-phase mixtures by explicit-implicit methods

Summary The one-dimensional equations for transient two-phase flow are a system of nonlinear hyperbolic partial differential equations, expressible, under certain assumptions, in conservation form. Inasmuch as the use of the method of characteristics becomes complicated if shock waves are present, it is easier to follow a gas-dynamics approach and employ one of the available procedures for solving one-dimensional systems of conservation equations. A recently introduced technique, due to McGuire and Morris [1, see also 12] and known as an Explicit-Implicit method, is used here for a simple boundary-value problem of wave propagation in bubbly two-phase mixtures, and is found to be simple and versatile. A comparison of this method with the well-known Lax-Wendroff (two-step) scheme demonstrates that shock fronts are simulated better, oscillations behind the shocks are smoothable by parameter adjustment, and computation time is reduced when the Explicit-Implicit method is employed.