Validation of a Computational Algorithm Based on the Discontinuous Galerkin Method for the Baer–Nunziato Relaxation Model

The Runge–Kutta/Discontinuous Galerkin (RK/DG) method is considered to simulate the dynamics of two-phase media in the framework of a completely nonequilibrium Baer–Nunziato model taking into account stiff mechanical relaxation. The WENO-S limiter is used to monotonize the solution. It is applied directly to the conservative variables of the model. Relaxation processes are modeled using the sixth-order implicit BDF (Backward Differentiation Formula) method with an adaptive choice of the integration step. An approach based on the DLM theory is used to construct the numerical flux. This theory permits one to generalize Godunov type methods to the case of nonconservative hyperbolic systems. One- and two-dimensional problems are calculated by means of the developed method, and the analysis of the calculation results is given. In the two-dimensional case, the calculation data are compared with the results of laboratory experiments.