An acoustic-transport splitting method for the barotropic Baer-Nunziato two-phase flow model

Abstract

This work focuses on the numerical approximation of the barotropic Baer-Nunziato two-phase flow model. We propose a numerical scheme that relies on an operator splitting method corresponding to a separate treatment of the acoustic and the material transport phenomena. In the subsonic case, this also corresponds to a separate treatment of the fast and the slow propagation phenomena. This approach follows the lines of the implicit-explicit schemes developed in [8]. The operator splitting enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, while maintaining accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms that figure in the two-phase model. We prove that the proposed numerical strategy is positivity preserving for the volume fractions and the partial masses. The scheme is tested against several one-dimensional test cases including flows featuring vanishing phases.