Sharp interface capturing godunov method for multi-material flow simulations

The Eulerian approach for calculating the reduced Baer-Nunziato model for multiphase fluid flows is considered. The model assumes equilibrium in pressure, temperature, and velocity and is known as P-V-T model in literature. The developed method refers to the class of interface capturing methods with material interfaces being diffused in space. The sharp capturing is attained by implementing (1) local face-based interface reconstruction, (2) flux approximation based on the solution to composite Riemann problem (CRP) - the conventional single material Riemann problem supplemented with a bi-material contact discontinuity, and (3) the AMR technique. An approximate CRP solver is proposed for the P-V-T model equations, which allows to consider interface transferring across cell faces. This method effectively alleviates numerical diffusion without introducing spurious oscillations; the interface resolution is found within one computational cell in 1D calculations. The octree dynamic AMR is implemented to enhance resolution of small-scale characteristics of the numerical solution. The performance and robustness of the method are demonstrated through several numerical tests of multi-fluid flow.