A comparison of hyperbolic solvers II: ausm-type and Hybrid Lax-Wendroff-Lax-Friedrichs methods for two-phase flows

Abstract

-Riemann-solver based schemes are difficult and sometimes impossible to be applied for complex flows due to the required average state. Other methods that do not use Riemann-solvers are best suited for such cases. Among them, AUSM+, AUSMDV and the recently proposed Hybrid Lax-Friedrichs-Lax-Wendroff (HLFW) have been extended to two-phase flows. The eigenstructure of the two-fluid model is complex due to the phase interactions, leading to numerous numerical difficulties. One of them is the well-posedness of the equation system because it may lose hyperbolicity. Therefore, the methods that are not based on the wave structure and that are not TVNI could lead to strong oscillations. The common strategy to handle this problem is the adoption of a pressure correction due to interfacial effects. In this work, this procedure was applied to HLFW and AUSM-type methods and their results analyzed. The AUSM+ and AUSMDV were extended to achieve second-order using the MUSCL strategy for which a conservative and a non-conservative formulation were tested. Additionally, several AUSMDV weighting functions were compared. The first and second-order AUSM-type and HLFW methods were compared for the solution of the water faucet and the shock tube benchmark problems. The pressure correction strategy was efficient to ensure hyperbolicity, but numerical diffusion increased. The MUSCL AUSMDV and HLFW methods with pressure correction strategy were, on average, the best of the analyzed methods for these test problems. The HLFW was more stable than the other methods when the pressure correction was considered.

Supersonic combustion of n-Heptane droplets with cavity-based fuel injection

“…The AUSM + method (Liou, 1996) has these features: Positivity preserving property, improvement in accuracy, simplicity and easy generalization to other conservation laws (Coelho, 2010). The particle phase is treated using Saurel's (1994) method.…”

Modeling and Simulation of Supersonic Flow in 2D Nozzle Using MacCormack’s and Upwind Methods

“…Liou (1996) proposed a modified scheme called AUSM+, which is capable of solving contact discontinuities exactly without non-monotonic problems. Besides, the method preserves the positivity of pressure, density and volume fraction [6].…”