Numerical solution of hyperbolic two-fluid two-phase flow model based on flux limiter centered TVD scheme

Purpose This study aims to develop and assess accurate finite difference methods for the numerical simulation of transient gas-liquid two-phase flow in pipelines based on the two-fluid model. Design/methodology/approach The two-fluid model is used to describe transient gas-liquid two-phase flow and a finite difference framework is developed for its numerical solution. The governing equations are first decomposed into a non-homogeneous system of ordinary differential equations (ODEs) and a homogeneous system of partial differential equations (PDEs) using the splitting scheme of the source term (SSST). The ODE system is integrated in time by the fourth-order Runge-Kutta (RK4) method. For the homogeneous PDEs, within the framework of the explicit Godunov finite difference discretization, the conservative term is discretized with the First-Order Centered (FORCE), Flux-Corrected Transport (FCT) and the proposed flux limiter centered Total Variation Diminishing (TVD-FLIC) schemes with Minbee and Superbee limiters, while the non-conservative terms are treated using the MINMOD scheme. The developed methods are validated using four representative benchmark problems, namely, Ransom’s water faucet case, the large relative velocity shock tube case, the modified shock tube case and Toumi’s water-air shock tube case. In addition, the developed methods are further assessed through an experimental water hammer case and a parametric study of flow and geometric conditions. Findings All numerical methods successfully reproduce the expected flow behavior in the benchmark problems and the hyperbolicity analysis confirms the applicability of the two-fluid model under the considered flow conditions. The accuracy assessment based on Toumi’s water-air shock tube case shows that the TVD-FLIC Superbee scheme provides the smallest relative error, whereas the FORCE scheme exhibits the largest error, with the FCT scheme yielding intermediate accuracy between the TVD-FLIC Minbee and Superbee schemes. Furthermore, the proposed TVD-FLIC Superbee scheme demonstrates superior convergence behavior and higher numerical accuracy than the widely adopted FCT scheme. Originality/value This work presents, for the first time, the application of the TVD-FLIC scheme with Minbee and Superbee limiters to the finite difference solution of the two-fluid model for transient gas-liquid pipeline flows. Compared with the commonly adopted FCT scheme, the proposed approach provides improved shock-capturing capability, higher accuracy and better convergence, offering an effective alternative for transient multiphase-flow simulations.