Adv. Appl. Math. Mech., 6 (2014), pp. 49-74.

On the Computations of Gas-Solid Mixture Two-Phase Flow

D. Zeidan 1*, R. Touma 2

1 Department of Mathematics, Al-Balqa Applied University, Al-Salt, Jordan
2 Department of Computer Science & Mathematics, Lebanese American University, Beirut, Lebanon

Received 23 May 2012; Accepted (in revised version) 24 May 2013
doi: 10.4208/aamm.12-m1282


This paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical model. The HLL Riemann solver is applied to solve the Riemann problem for the model equations. This solution is then employed in the construction of upwind Godunov methods to solve the general initial-boundary value problem for the two-phase gas-solid mixture. Several representative test cases have been carried out and numerical solutions are provided in comparison with existing numerical results. To demonstrate the robustness, effectiveness and capability of these methods, the model results are compared with reference solutions. In addition to that, these results are compared with the results of other simulations carried out for the same set of test cases using other numerical methods available in the literature. The diverse comparisons demonstrate that both the model equations and the numerical methods are clear in mathematical and physical concepts for two-phase fluid flow problems.

AMS subject classifications: 76T15, 76N10, 35L65, 65M08
Key words: Hyperbolic conservative equations, two-phase flows, compressible gas-solid, mixture conservation laws, approximate Riemann solver, upwind Godunov methods, numerical simulation.

*Corresponding author.
Email:, diazeidan@gmail/ (D. Zeidan)

The Global Science Journal