Influence of Interfacial Pressure Term on the Hyperbolicity of a General Multifluid Model

The multifield model like its counterpart, the two-fluid model, generally fails to be hyperbolic in its basic formulation. However, interfacial forces such as the interfacial pressure term and the virtual mass force, bringing new differential terms to the system, can change the analysis and make the problem hyperbolic. The aim of this paper is to define how the interfacial pressure default force affects the hyperbolicity of a general multifield model, and consequently, its inherent numerical stability. We characterize the location of the non hyperbolic regions and propose a closure for the interfacial pressure that makes the system hyperbolic in physically relevant regions.