The Riemann problem for the nonisentropic Baer-Nunziato model of two-phase flows. (English) Zbl 1491.35290
Summary: The Riemann problem for the well-known Baer-Nunziato model of two-phase flows is solved. The system consists of seven partial differential equations with nonconservative terms. The most challenging problem is that this model possesses a double eigenvalue. Although characteristic speeds coincide, the curves of composite waves associated with different characteristic fields can be still constructed. They will also be incorporated into composite wave curves to form solutions of the Riemann problem. Solutions of the Riemann problem will be constructed when initial data are in supersonic regions, subsonic regions, or in both kinds of regions. A unique solution and solutions with resonance are also obtained.
MSC:
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35L60 | First-order nonlinear hyperbolic equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 76T99 | Multiphase and multicomponent flows |
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