We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase
flow model, that is able to cope with arbitrarily small values of the statistical phase
fractions. The solver relies on a relaxation approximation of the model for which the
Riemann problem is exactly solved for subsonic relative speeds. In an original manner, the
Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate
the total energy in the vanishing phase regimes, thereby enforcing the robustness and
stability of the method in the limits of small phase fractions. The scheme is proved to
satisfy a discrete entropy inequality and to preserve positive values of the statistical
fractions and densities. The numerical simulations show a much higher precision and a more
reduced computational cost (for comparable accuracy) than standard numerical schemes used
in the nuclear industry. Finally, two test-cases assess the good behavior of the scheme
when approximating vanishing phase solutions.