On the computation of the Baer–Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid–structure interactions

Computation of compressible two-phase flows with the unsteady compressible Baer–Nunziato model in conjunction with the moving grid approach is discussed in this paper. Both HLL- and HLLC-type Finite-Volume methods are presented and implemented in the context of Arbitrary Lagrangian–Eulerian formulation in a multidimensional framework. The construction of suitable numerical methods is linked to proper approximations of the non-conservative terms on moving grids. The HLL discretization follows global conservation properties such as free-stream preservation and uniform pressure and velocity profiles preservation on moving grids. The HLLC solver initially proposed by Tokareva and Toro [1] for the Baer–Nunziato model is based on an approximate solution of local Riemann problems containing all the characteristic fields present in the exact solution. Both “subsonic” and “supersonic” configurations are considered in the construction of the present HLLC solver. In addition, an adaptive 6-wave HLLC scheme is also proposed for computational efficiency. The methods are first assessed on a variety of 1-D Riemann problems including both fixed and moving grids applications. The methods are finally tested on 2-D and 3-D applications: 2-D Riemann problems, a 2-D shock–bubble interaction and finally a 3-D fluid–structure interaction problem with a good agreement with the experiments.