Assessment of mixture two-phase flow equations for volcanic flows using Godunov-type methods

This paper is concerned with the numerical solution of the equations governing two-phase gas-magma mixture in the framework of thermodynamically compatible systems theory. The equations constitute a non-homogeneous system of nonlinear hyperbolic conservation laws. A total variation diminishing (TVD) slope limiter center (SLIC) numerical scheme, based on the Riemann problem, is presented and applied for the solution of the initial boundary value problem for the equations. The model equations and the numerical methods are systematically assessed through a series of numerical test cases. Simulation results are compared and validated with different model equations available in the literature. The computed results compare well with the exact results provided for validation. Strong evidence shows that the model and the methods are accurate, robust and conservative. The model correctly describes the formation of shocks and rarefactions in two-phase gas-magma flow.