Numerical simulation of shock wave – dense particles cloud interaction using Godunov solver for Baer–Nunziato equations

Abstract

PurposeThis paper aims to clarify some aspects of the application of the Godunov method for the Baer–Nunziato equations solution on the example of the problem of shock wave – dense particles cloud interaction.Design/methodology/approachThe statement of the problem corresponds to the natural experiment. Mathematical model is based on the Baer–Nunziato system of equations with algebraic right-hand side source terms that takes into account the interphase friction force. Two numerical approaches are used: Harten-Lax-van Leer method and Godunov method.FindingsFor the robust simulation using Godunov method, the application of the pressure relaxation procedure is proposed. The comparative analysis of the simulation results using two methods is carried out. The Godunov method provides significantly smaller numerical diffusion of the solid phase volume fraction in the cloud that leads to the much better agreement of the pressure curves on transducers and the dynamics of the cloud motion with the experimental data.Originality/valueGodunov method for the Baer–Nunziato equations is applied for the simulation of the natural experiment on the shock wave particles cloud interaction. Up to now, the examples of the application of the Godunov method for the Baer–Nunziato equations to the investigation of the practical problems have been limited by the works of the authors of the method and the field of detonation in the heterogeneous explosives. For the robust simulations in the presence of interphase boundaries, it is proposed to use the Godunov method together with the pressure relaxation procedure.