Computations of two-fluid models based on a simple and robust hybrid primitive variable Riemann solver with AUSMD

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• 作者：Yang-Yao Niu ^{yyniu@mail.tku.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primitive variable Riemann solver ; AUSMD ; Two-fluid model ; Multi-phase flows
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：308
• 期：Complete
• 页码：389-410
• 全文大小：3067 K

文摘

This paper is to continue our previous work in 2008 on solving a two-fluid model for compressible liquid–gas flows. We proposed a pressure–velocity based diffusion term original derived from AUSMD scheme of Wada and Liou in 1997 to enhance its robustness. The proposed AUSMD schemes have been applied to gas and liquid fluids universally to capture fluid discontinuities, such as the fluid interfaces and shock waves, accurately for the Ransom's faucet problem, air–water shock tube problems and 2D shock–water liquid interaction problems. However, the proposed scheme failed at computing liquid–gas interfaces in problems under large ratios of pressure, density and volume of fraction. The numerical instability has been remedied by Chang and Liou in 2007 using the exact Riemann solver to enhance the accuracy and stability of numerical flux across the liquid–gas interface. Here, instead of the exact Riemann solver, we propose a simple AUSMD type primitive variable Riemann solver (PVRS) which can successfully solve 1D stiffened water–air shock tube and 2D shock–gas interaction problems under large ratios of pressure, density and volume of fraction without the expensive cost of tedious computer time. In addition, the proposed approach is shown to deliver a good resolution of the shock-front, rarefaction and cavitation inside the evolution of high-speed droplet impact on the wall.