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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  2. Ji, Junze; Li, Zhufei; Zhang, Enlai; Si, Dongxian; Yang, Jiming: Intensification of non-uniformity in convergent near-conical hypersonic flow (2022)
  3. Moghimi, Mohsen H.; Quinlan, Nathan J.: Application of finite volume particle method for axisymmetric modeling of droplet formation in dripping and Rayleigh regimes (2022)
  4. Wang, Miao-Miao; Wu, Zi-Niu: Reflection of rightward moving shocks of the first and second families over a steady oblique shock wave (2022)
  5. Xie, Wenjia; Tian, Zhengyu; Zhang, Ye; Yu, Hang; Ren, Weijie: A unified construction of all-speed HLL-type schemes for hypersonic heating computations (2022)
  6. Golovin, D. V.: Numerical simulation of sound pressure for calibration system of \textitLStype measurement microphones (2021)
  7. Ladonkina, M. E.; Neklyudova, O. A.; Tishkin, V. F.: Hybrid numerical flux for solving the problems of supersonic flow of solid bodies (2021)
  8. Mamashita, Tomohiro; Kitamura, Keiichi; Minoshima, Takashi: SLAU2-HLLD numerical flux with wiggle-sensor for stable low Mach magnetohydrodynamics simulations (2021)
  9. Manueco, Lucas; Weiss, Pierre-Élie; Deck, Sébastien: On the coupling of wall-model immersed boundary conditions and curvilinear body-fitted grids for the simulation of complex geometries (2021)
  10. Pandare, Aditya K.; Waltz, Jacob; Bakosi, Jozsef: Multi-material hydrodynamics with algebraic sharp interface capturing (2021)
  11. Reynaud, J.; Weiss, P.-E.; Deck, S.: Numerical workflow for scale-resolving computations of space launcher afterbody flows with and without jets (2021)
  12. Sandhu, Jatinder Pal Singh; Ghosh, Santanu: A local correlation-based zero-equation transition model (2021)
  13. Spinelli, Gregorio Gerardo; Celik, Bayram: Applications of a central ENO and AUSM schemes based compressible N-S solver with reconstructed conservative variables (2021)
  14. Sun, Di; Qu, Feng; Liu, Qingsong; Zhong, Jiaxiang: Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows (2021)
  15. Yoo, Young-Lin; Sung, Hong-Gye: A hybrid AUSM scheme (HAUS) for multi-phase flows with all Mach numbers (2021)
  16. 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)
  17. Cheng, Jian; Zhang, Fan; Liu, Tiegang: A discontinuous Galerkin method for the simulation of compressible gas-gas and gas-water two-medium flows (2020)
  18. 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)
  19. Chen, Shusheng; Lin, Boxi; Li, Yansu; Yan, Chao: HLLC+: low-Mach shock-stable HLLC-type Riemann solver for all-speed flows (2020)
  20. 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)

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