Riemann solver for the Nigmatulin model of two-phase flow

The two-phase model of Nigmatulin (Dynamics of Multiphase Media, 1991) is revisited and a second order Godunov solver is constructed for the corresponding Riemann problem using a seven wave structure. This model differs from the well established Baer-Nunziato model (International J. Multiphase Flow, Vol. 12, No. 6, 1986, pp. 861-889) in that it treats the solid phase as incompressible, and also accounts for thermal as well as elastic energies for the solid phase. Numerical results are presented for three classes of Riemann problems, demonstrating the accuracy of the method. The effect of inter-granular stress on the flow physics is investigated and it is shown that this term results in faster wave speeds for higher stresses. This study confirms that the Nigmatulin model can also be useful for the study of two-phase flows.