On the formulation of the virtual mass term in two fluid models

Abstract

Quantitative bounds on coefficients of the virtual mass terms were derived for mathematical hyperbolicity and satisfaction of the Second Law of Thermodynamics. The recommended bounds for the coefficients in the present analysis are of a simple and clear nature. One-dimensional numerical simulation showed that a suggested criterion for stability predicts well the onset of instability. It is also concluded that an interfacial momentum transfer term composed of drag and virtual mass terms need not violate the Second Law. Therefore the resulting interfacial momentum term is simpler than recommended by previous studies. © 1986.