A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow. (English) Zbl 1415.76480
Summary: Here, we extend the Toro-Vázquez flux vector splitting approach (TV), originally proposed for the ideal 1D Euler equations in [E. F. Toro and M. E. Vázquez-Cendón, Comput. Fluids 70, 1–12 (2012; Zbl 1365.76243)], to the Baer-Nunziato equations of compressible two-phase flow. Following the TV approach, we identify corresponding advection and pressure operators. We perform a rigorous analysis of the associated non-conservative pressure system and derive its complete characteristic structure. The choice of the advection numerical flux is obvious. For the pressure system, several schemes are presented. The complete schemes are then implemented in the setting of finite volume and path-conservative methods and are systematically assessed in terms of accuracy and efficiency, through a carefully selected suite of test problems. The presented schemes constitute a building block for the construction of high-order numerical methods for solving the Baer-Nunziato equations. Here, as an illustrative example of such possibility, we present the construction of a second-order scheme.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76T15 | Dusty-gas two-phase flows |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
Citations:
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