Efficient second-order accurate shock-capturing scheme for modeling one- and two-phase water hammer flows

This paper focuses on the formulation and assessment of a second-order accurate finite volume (FV) shock-capturing scheme for simulating one- and two-phase water hammer flows. The two-phase flow model is based on the single-equivalent fluid concept. The proposed scheme for one- and two-phase flows is the same, except for the Riemann solvers used to evaluate fluxes between computational cells. For one-phase flows, the accuracy and numerical efficiency of the proposed scheme is contrasted against the fixed-grid method of characteristics (MOC) and a recently proposed FV scheme. For two-phase flows, the accuracy and numerical efficiency of the proposed scheme are compared to the fixed-grid MOC scheme. The results for one-phase flows show that, when a Courant number (Cr) very close to 1.0 (around 0.99 or higher) is used, the MOC scheme is more efficient than the proposed scheme and the other FV scheme. In this case, the latter two schemes have similar numerical efficiency. When Cr drops below about 0.95, the proposed scheme is more efficient than the MOC scheme and the other FV scheme, especially for smooth transient flows (no discontinuities). For two-phase water hammer flows, all the simulations were carried out using a maximum Courant number of 0.95 to avoid numerical instability problems. The results for two-phase flows show that the proposed scheme is much more efficient than the fixed-grid MOC scheme. The fixed-grid MOC and the proposed scheme are also used to reproduce a set of two-phase flow experiments reported in the literature. Good agreement between simulated and experimental data is found.