A sequel to AUSM II: AUSM + -up for all speeds. We present ideas and procedure to extend the AUSM-family schemes to solve flows at all speed regimes. To achieve this, we first focus on the theoretical development for the low Mach number limit. Specifically, we employ asymptotic analysis to formally derive proper scalings for the numerical fluxes in the limit of small Mach number. The resulting new scheme is shown to be simple and remarkably improved from previous schemes in robustness and accuracy. The convergence rate is shown to be independent of Mach number in the low Mach number regime up to M ∞ =0·5, and it is also essentially constant in the transonic and supersonic regimes. Contrary to previous findings, the solution remains stable, even if no local preconditioning matrix is included in the time derivative term, albeit a different convergence history may occur. Moreover, the new scheme is demonstrated to be accurate against analytical and experimental results. In summary, the new scheme, named AUSM+-up, improves over previous versions and eradicates fails found therein.

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  1. Ladonkina, M. E.; Neklyudova, O. A.; Tishkin, V. F.: Hybrid numerical flux for solving the problems of supersonic flow of solid bodies (2021)
  2. Pandare, Aditya K.; Waltz, Jacob; Bakosi, Jozsef: Multi-material hydrodynamics with algebraic sharp interface capturing (2021)
  3. Sandhu, Jatinder Pal Singh; Ghosh, Santanu: A local correlation-based zero-equation transition model (2021)
  4. Sun, Di; Qu, Feng; Liu, Qingsong; Zhong, Jiaxiang: Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows (2021)
  5. Bocharov, A. N.; Evstigneev, N. M.; Petrovskiy, V. P.; Ryabkov, O. I.; Teplyakov, I. O.: Implicit method for the solution of supersonic and hypersonic 3D flow problems with lower-upper symmetric-Gauss-Seidel preconditioner on multiple graphics processing units (2020)
  6. Cheng, Jian; Zhang, Fan; Liu, Tiegang: A discontinuous Galerkin method for the simulation of compressible gas-gas and gas-water two-medium flows (2020)
  7. Chen, Shu-sheng; Cai, Fang-jie; Xue, Hai-chao; Wang, Ning; Yan, Chao: An improved AUSM-family scheme with robustness and accuracy for all Mach number flows (2020)
  8. Chen, Shusheng; Lin, Boxi; Li, Yansu; Yan, Chao: HLLC+: low-Mach shock-stable HLLC-type Riemann solver for all-speed flows (2020)
  9. Chung, Joseph D.; Zhang, Xiao; Kaplan, Carolyn R.; Oran, Elaine S.: The barely implicit correction algorithm for low-Mach-number flows. II: Application to reactive flows (2020)
  10. D’Alessandro, Valerio; Falone, Matteo; Ricci, Renato: Direct computation of aeroacoustic fields in laminar flows: solver development and assessment of wall temperature effects on radiated sound around bluff bodies (2020)
  11. Ejtehadi, Omid; Myong, R. S.: A modal discontinuous Galerkin method for simulating dusty and granular gas flows in thermal non-equilibrium in the Eulerian framework (2020)
  12. Fleischmann, Nico; Adami, Stefan; Hu, Xiangyu Y.; Adams, Nikolaus A.: A low dissipation method to cure the grid-aligned shock instability (2020)
  13. Fu, Kai; Deng, Xiaolong; Jiang, Lingjie; Wang, Pengfei: Direct numerical study of speed of sound in dispersed air-water two-phase flow (2020)
  14. Iampietro, D.; Daude, F.; Galon, P.: A low-diffusion self-adaptive flux-vector splitting approach for compressible flows (2020)
  15. Kitamura, Keiichi; Mamashita, Tomohiro; Ryu, Dongsu: SLAU2 applied to two-dimensional, ideal magnetohydrodynamics simulations (2020)
  16. Li, Zhiyong; Tang, Tingting; Liu, Yu; Arcondoulis, Elias J. G.; Yang, Yannian: Implementation of compressible porous-fluid coupling method in an aerodynamics and aeroacoustics code. II: Turbulent flow (2020)
  17. Li, Zhiyong; Zhang, Huaibao; Liu, Yu; McDonough, James M.: Implementation of compressible porous-fluid coupling method in an aerodynamics and aeroacoustics code. I: Laminar flow (2020)
  18. Manokaran, K.; Ramakrishna, M.; Jayachandran, T.: Application of flux vector splitting methods with \textitSSTturbulence model to wall-bounded flows (2020)
  19. Manueco, Lucas; Weiss, Pierre-Elie; Deck, Sébastien: On the estimation of unsteady aerodynamic forces and wall spectral content with immersed boundary conditions (2020)
  20. Moguen, Yann; Dick, Erik: Diffusion and dissipation in acoustic propagation simulation by convection-pressure split algorithms in all Mach number form (2020)

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