A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow

Here we extend the Toro-Vázquez flux vector splitting approach (TV), originally proposed for the ideal 1D Euler equations in [1], 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.