Abstract
Recently, much attention has been given to the study of mixed systems of conservation laws, in which evolutionary systems of partial differential equations have the property that some of their eigenvalues are complex. This has led to some confusion, particularly in the field of two-phase flow, in which the correct form of the governing equations for different flow regimes is not clear. In this study we consider two mixed systems, one being a 2 x 2 system in which the analytic solution is known if certain special waves are defined and the other a prototype system of equations for modelling single-pressure two-phase flow. By using these examples it is shown both analytically and by numerical experiment that solving such sets of equations is far from an easy matter. The results have implications for the modelling of two-phase flows and other mixed systems, suggesting that although in some cases it might be possible to calculate solutions successfully, great care is generally needed in interpreting numerical results. This emphasizes the continuing requirement for more detailed mathematical modelling of two-phase flows.
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