To overcome the numerical difficulties of the density-based method for low-Mach-number two-phase flow, this paper adopts the AUSM(+) and AUSMDV schemes based on a staggered-grid arrangement. The water faucet, air-water shock tube, oscillating manometer and air-water phase separation problems are used as benchmark tests to validate the implementation of the generic four-equation two-fluid model. The present results reveal the advantages of using staggered-grid-based AUSM(+) and AUSMDV schemes over the collocated-grid-based counterpart. With a staggered-grid arrangement, odd-even decoupling issues can be avoided. Thus, no sound speed scaling or additional diffusion terms are needed when using AUSM(+) and AUSMDV schemes for low-Mach-number two-phase flow. Furthermore, since the pressure and void fraction are already stored at the interface of the velocity control volume, no interpolation of interfacial pressure is needed for momentum equations. Finally, this study will help integrate AUSM(+) and AUSMDV schemes into staggered-grid-based thermal hydraulic codes, e.g. CATHENA, used in the nuclear industry. Moreover, to tackle the stiffness issues in relation to phase appearance and disappearance, we propose a new staggered-grid-based scheme referred to as AUSMFVS, which combines the accuracy of AUSM+ and the stability of FVS. (C) 2017 Elsevier Ltd. All rights reserved.