Hyperbolicity Criteria for System of Field Equations of One-Dimensional Two-Phase Flow with Compressible Components

As part of an effort to improve the stability of the RELAP5-3D computer code, a characteristic analysis of the governing differential equations for a compressible, one-dimensional, two-fluid, nonhomogeneous nonequilibrium model is presented. The study is limited to the case when small timescale relaxation terms can be neglected, and therefore, a two-pressure model can be reduced to an equivalent volume-average, one-pressure model. The primary focus of the work is to consider flow with compressible components and to compare hyperbolicity criteria with the results of commonly used limitations of flow with incompressible phases. Based on a review of current achievements in this area, a generic form of momentum conservation equations that are invariant from the definition of differential interfacial terms is suggested. New analytical criteria of strict hyperbolicity of the governing system for the compressible two-phase-flow model are developed and supported by numerical calculations and comparisons. Furthermore, overrestriction of results of eigenvalue analysis based on an incompressible components model is demonstrated.

The derived criteria are applied to RELAP5-3D in the form of modifications to momentum equations. Upon implementing the developed criteria, the simulation results show marked improvement in stability without otherwise affecting the calculations. The importance of well-posedness of the initial value problem for numerical solution stability is demonstrated.