A relaxation scheme for hybrid modelling of gas-particle flows

► A new relaxation technique to simulate a hybrid two-phase flow model. ► Verification of the scheme for barotropic Euler equations. ► Energy estimates for the relaxation system. ► Numerical results with non-smooth external data provided to the model. This paper aims at proposing a relaxation scheme that allows to obtain stable approximations for a system of partial differential equations which governs the evolution of the void fraction and the mean velocity in the particle phase of two-phase flows. This system involves the divergence of a particle kinetic tensor, which is provided by a Lagrangian code and whose components are not smooth. The simulation algorithm is based on the combined use of upwinding and relaxation techniques. The main properties of the method are given, together with the Finite Volume Godunov scheme and this approach is compared to an analogous one that was developed earlier. Some measured rates of convergence in L1-norm are provided, for a particular choice of the kinetic tensor. To complete the picture, we present some numerical results obtained when non-smooth external data are provided to the system.