Numerical Approximation for a One-Dimensional Two-Phase Mixture Conservation Laws

An alternative to currently used two-phase flow equations is considered to resolve discontinuous solutions in gas-solid mixtures. The equations in the present paper are based on the theory of thermodynamically compatible systems of hyperbolic conservation laws. The conservative hyperbolic governing equations were solved using Godunov methods of centred-type. This solution is then employed in the source terms problem with Strang splitting technique to solve the general initial-value problem for the two-phase flow equations. Results are presented, demonstrating the accuracy of the numerical methods associated with of the proposed two-phase conservation laws.