Hyperbolicity, Discontinuities and Numerics of the Two-Fluid Model

Abstract

The hyperbolicity boundaries of a (droplet) disperse, two-phase flow model at high flow speeds and relative velocities are found, the role of interfacial pressure on regularization is discussed, and the effects on integrability of the system of equations, solver robustness, and convergence properties are determined as a function of position relative to hyperbolic boundaries. We find good agreement between model and physics in that both exhibit a “sensitive” behavior in the transonic region (relative Mach number ∼1, hereafter omitting “relative” for brevity), and in that regularization requires increasing the interfacial pressure coefficient consistently with flow peculiarities in this region. The result is a two-phase flow model that is unconditionally hyperbolic and robust to grid refinement even in the most sensitive numerical tests with no dissipative terms in the equations.