Simple and robust HLLC extensions of two-fluid AUSM for multiphase flow computations

• We present simple extensions of a two-fluid Godunov-AUSM solver to an HLLC–AUSM.
• The two-fluid HLLC–AUSM is proven as robust as the Godunov-AUSM.
• It is achieved when velocity and pressure in the middle zone are computed by HLLC.
• The present method is free from iterations and convergence criteria.
• It is applicable to a challenging, water-shock/air-bubble interaction.

A two-fluid AUSM+-up numerical flux function with the exact (Godunov) Riemann solver for the stratified flow model concept by Chang et al. (2007) has been extended for simple and robust computations of compressible multiphase flows. The present method replaces the Godunov part with the HLLC approximate Riemann solver with no-iteration procedure in a very simple manner: This two-fluid HLLC has been inspired by the work by Hu et al. (2009), but used in a totally different way. Numerical tests demonstrate that the present two-fluid AUSM+-up is, if only velocity and pressure in the middle zone are computed by HLLC, as robust as the original, Godunov-combined AUSM+-up, despite being free from iterations and convergence criteria.