In this paper we present a methodology for constructing accurate
and efficient hybrid central-upwind (HCU) type schemes for
the numerical resolution of a two-fluid model commonly used by the
nuclear and petroleum industry. Particularly, we propose a method
which does not make use of any information about the
eigenstructure of the Jacobian matrix of the model.
The two-fluid model possesses a highly nonlinear pressure law.
From the mass conservation equations we develop an evolution
equation which describes how pressure evolves in time. By applying
a quasi-staggered Lax-Friedrichs type discretization for this
pressure equation together with a Modified Lax-Friedrich type
discretization of the convective terms, we obtain a central type
scheme which allows to cope with the nonlinearity (nonlinear
pressure waves) of the two-fluid model in a robust manner.
Then, in order to obtain an accurate resolution of mass fronts, we
employ a modification of the convective mass fluxes by hybridizing
the central type mass flux components with upwind type components.
This hybridization is based on a splitting of the mass fluxes into
components corresponding to the pressure and volume fraction
variables, recovering an accurate resolution of a contact
In the numerical simulations, the resulting HCU scheme gives
results comparable to an approximate Riemann solver while being
superior in efficiency. Furthermore, the HCU scheme yields better
robustness than other popular Riemann-free upwind schemes.