Schemes to compute unsteady flashing flows

Some ways to compute flashing flows in variable cross section ducts are provided, focusing on the homogeneous relaxation model. The basic numerical method relies on a splitting technique that is consistent with the overall entropy inequality. The cross section is assumed to be continuous, and the finite volume approach is applied to approximate homogeneous equations. Several suitable schemes to account for complex equation of state are discussed, namely, the Rusanov scheme, an approximate form of the Roe scheme, and the "volumes finis Roe" (VFRoe) scheme with the help of nonconservative variables. To evaluate respective accuracy, the homogeneous Enter equations are computed first, and the L1 error norm of transient solutions of shock tube experiments are plotted. It is shown that the Rusanov scheme is indeed less accurate, which balances its interesting properties, inasmuch as it preserves the positivity of the mean density and the maximum principle for the vapor quality. Computations of real cases are presented, which account for the mass transfer term and the time-space dependent cross sections.