Effects of Virtual Mass on the Mathematical Characteristics and Numerical Stability of the Two-Fluid Model

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Abstract
It is known that the typical six-equation two-fluid model of two-phase flow possesses complex characteristics, exhibits unbounded instabilities in the short-wavelength limit, and constitutes an ill-posed initial value problem. The conditions under which the virtual mass force term helps to overcome these difficulties were studied. Quantitative bounds on coefficients of the virtual mass terms were derived for mathematical hyperbolicity, numerical stability, and satisfaction of the second law of thermodynamics. One-dimensional numerical simulation showed that the suggested inequality for numerical stability predicts well the onset of instability. Also it was found that a growing instability may be possible if interfacial friction is not enough to stabilize the growing modes.

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