Extension and Comparative Study of AUSM-Family Schemes for Compressible Multiphase Flow Simulations

Several recently developed AUSM-family numerical flux functions (SLAU, SLAU2, AUSMM + -up2, and AUSMPW+) have been successfully extended to compute compressible multiphase flows, based on the stratified flow model concept, by following two previous works: one by M.-S. Liou, C.-H. Chang, L. Nguyen, and T.G. Theofanous [AIAA J. 46:2345-2356, 2008], in which AUSM + -up was used entirely, and the other by C.-H. Chang, and M.-S. Liou [J. Comput. Phys. 225:840-873, 2007], in which the exact Riemann solver was combined into AUSM+-up at the phase interface. Through an extensive survey by comparing flux functions, the following are found: (1) AUSM + -up with dissipation parameters of K p and K u equal to 0.5 or greater, AUSMPW+, SLAU2, AUSM+-up2, and SLAU can be used to solve benchmark problems, including a shock/water-droplet interaction; (2) SLAU shows oscillatory behaviors [though not as catastrophic as those of AUSM + (a special case of AUSM + -up with Kp = K u = 0)] due to insufficient dissipation arising from its ideal-gas-based dissipation term; and (3) when combined with the exact Riemann solver, AUSM + -up ( K p = K u = 1), SLAU2, and AUSMPW+ are applicable to more challenging problems with high pressure ratios.

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