Extension and Comparative Study of AUSM-Family Schemes for Compressible Multiphase Flow Simulations
Keiichi Kitamura 1*, Meng-Sing Liou 2, Chih-Hao Chang 31 NASA Glenn Research Center, Cleveland, OH 44135, USA; Research Fellow of Japan Society for the Promotion of Science (JSPS), JAXA's Engineering Digital Innovation (JEDI) Center, 3-1-1 Yoshinodai, Chuo, Sagamihara, Japan; Previously at Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603 Japan; Currently at Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan.
2 NASA Glenn Research Center, Cleveland, OH 44135, USA.
3 Theofanous & Co Inc. Santa Barbara, CA 93109, USA.
Received 2 August 2013; Accepted (in revised version) 19 February 2014
Available online 24 June 2014
Several recently developed AUSM-family numerical flux functions (SLAU, SLAU2, AUSM+-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 K_p = 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.AMS subject classifications: 76T10, 76M12, 76N99
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Key words: Multiphase flow, two-fluid model, AUSM-family, stratified flow model.
Email: email@example.com (K. Kitamura), firstname.lastname@example.org (M.-S. Liou), email@example.com (C.-H. Chang)