A 1-D/3-D coupling approach for compressible non-equilibrium two-phase flows using the Baer-Nunziato model based on the Finite-Volume framework

Abstract

An efficient bi-directional 1-D/3-D coupling is here proposed for the computation of compressible two-phase flows with the use of the Baer-Nunziato model. The objective is here to couple the 3-D Baer-Nunziato model with its 1-D counterpart involving spatially varying pipe cross-sections. The present coupling acts at the common interface between three-dimensional and one-dimensional computational domains. The proposed approach is built upon the framework of the Finite-Volume method with, in particular, the exchange of the numerical fluxes coming from the approximation of both conservative and non-conservative terms of the convective part of the Baer-Nunziato model. For this purpose, local Riemann problems at the 1-D/3-D common interface are considered for the computation of the corresponding numerical conservative and non-conservative fluxes. These local Riemann problems are based on the variables associated with the 1-D domain on one side and the variables coming from the 3-D domain on the other side of the interface. The potentially non-null tangential phasic velocity components coming from the 3-D domain at the coupling interface are also considered in the local Riemann problems. In addition, adequate approximations of the non-conservative terms associated with changes of volume fraction as well as changes of cross-section are considered at the 1-D/3-D interface. As a consequence, conservation properties such as the uniform pressure and velocity profiles preservation are ensured by the present 1-D/3-D coupling. The pipe cross-section variations are also taken into account in the present method. What is more, no iterative procedure is required in the proposed approach. Several numerical shock-tubes involving both subsonic and supersonic configurations of the Baer-Nunziato model and pipe cross-section variations are then considered to assess the present 1-D/3-D coupling. The influence of the angle between the 1-D and the 3-D domains at the coupling interface is also studied. Finally, the propagation of a shock-wave in a circular tube with a sudden change in cross-section is simulated using a hybrid 1-D/3-D computation showing the potential of the proposed geometrical multi-scale strategy.