AbstractThe purpose of this article is to explain in more detail some ideas used recently by the authors to construct a class of hybrid explicit–implicit schemes for solving the two‐fluid model relevant for well and pipe flow simulations (Evje and Flåtten, SIAM J Sci Comput 26 (2005), 1449–1484; Evje and Flåtten, ESIAM: Math Mod Num Anal 39 (2005), 253–274; Evje and Flåtten, J Sci Comput, to appear). We here propose a framework which allows us to implement these ideas for a general system of hyperbolic conservation laws ut + f(u)x = 0. Main ingredients in this construction are (i) a splitting f(u) = g(u) + h(u) of the given flux function f; (ii) a corresponding decomposition of the original set of equations into two subsystems, one set of equations associated with the g flux, another with the h flux; (iii) inclusion of a set of flux evolution equations associated with the flux component h.We demonstrate that a sound and consistent discretization of this extended system gives rise to a class of central schemes which contains as a special case, corresponding to the splitting g = h = $1 \over 2$f, the FORCE scheme studied by Toro (Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer‐Verlag, Berlin, 1999). This justifies referring to the proposed class as eXtended FORCE (X‐FORCE). We discuss basic properties of the X‐FORCE class for nonlinear scalar conservation laws. By exploiting that the X‐FORCE schemes can be interpreted through Riemann solutions, we construct higher order X‐FORCE schemes by closely following along the line of the nonstaggered NT scheme presented in (Jiang et al., SIAM J Num Anal 35 (1998), 2147–2168). Characteristic behavior of various X‐FORCE schemes is demonstrated through calculation of numerical examples. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008