Аннотация:In this paper we firstly carry out an extension of the finite-volume WENO schemes to three space dimensions andhigher orders of accuracy. Secondly, we propose to use more accurate fluxes as the building block. These are the HLLCand MUSTA fluxes [Multi-stage predictor–corrector fluxes for hyperbolic equations, 2003; Restoration of the contactsurface in the HLL Riemann solver, Report CoA 9204, June 1992; J. Shock Waves 4 (1994) 25]. The numerical resultssuggest that the new WENO-HLLC and WENO-MUSTA schemes compare satisfactorily with the state-of-the-artfinite-volume scheme of Shi et al. [J. Comput. Phys. 175 (2002) 108].