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. 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)
  2. 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)
  3. Ching, Eric J.; Lv, Yu; Gnoffo, Peter; Barnhardt, Michael; Ihme, Matthias: Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows (2019)
  4. Labourasse, E.: A low-Mach correction for multi-dimensional finite volume shock capturing schemes with application in Lagrangian frame (2019)
  5. Li, Xintao; Lyu, Zhen; Kou, Jiaqing; Zhang, Weiwei: Mode competition in galloping of a square cylinder at low Reynolds number (2019)
  6. Moghimi, Mohsen H.; Quinlan, Nathan J.: Application of background pressure with kinematic criterion for free surface extension to suppress non-physical voids in the finite volume particle method (2019)
  7. Moghimi, Mohsen H.; Quinlan, Nathan J.: A model for surface tension in the meshless finite volume particle method without spurious velocity (2019)
  8. Tiam Kapen, Pascalin; Ghislain, Tchuen: A robust rotated-hybrid Riemann scheme for multidimensional inviscid compressible flows (2019)
  9. Chamarthi, Amareshwara Sainadh; Komurasaki, Kimiya; Kawashima, Rei: High-order upwind and non-oscillatory approach for steady state diffusion, advection-diffusion and application to magnetized electrons (2018)
  10. Chen, Shu-Sheng; Yan, Chao; Lin, Bo-Xi; Liu, Li-Yuan; Yu, Jian: Affordable shock-stable item for Godunov-type schemes against carbuncle phenomenon (2018)
  11. Chen, Shu-sheng; Yan, Chao; Xiang, Xing-hao: Effective low-Mach number improvement for upwind schemes (2018)
  12. Deck, Sébastien; Weiss, Pierre-Elie; Renard, Nicolas: A rapid and low noise switch from RANS to WMLES on curvilinear grids with compressible flow solvers (2018)
  13. Deng, Xiao-Long; Li, Maojun: Simulating compressible two-medium flows with sharp-interface adaptive Runge-Kutta discontinuous Galerkin methods (2018)
  14. Deng, Xi; Inaba, Satoshi; Xie, Bin; Shyue, Keh-Ming; Xiao, Feng: High fidelity discontinuity-resolving reconstruction for compressible multiphase flows with moving interfaces (2018)
  15. Deryugin, Yu. N.; Emel’yanova, Ya. V.; Zhuchkov, R. N.; Utkina, A. A.: Hybrid dissipation scheme as applied to computational aeroacoustics (2018)
  16. Dimarco, Giacomo; Loubère, Raphaël; Michel-Dansac, Victor; Vignal, Marie-Hélène: Second-order implicit-explicit total variation diminishing schemes for the Euler system in the low Mach regime (2018)
  17. Fürst, Jiří: Development of a coupled matrix-free LU-SGS solver for turbulent compressible flows (2018)
  18. Gastaldo, Laura; Herbin, Raphaèle; Latché, Jean-Claude; Therme, Nicolas: A MUSCL-type segregated -- explicit staggered scheme for the Euler equations (2018)
  19. Herbin, Raphaèle; Latché, Jean-Claude; Nguyen, Trung Tan: Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations (2018)
  20. Kinzel, Michael P.; Lindau, Jules W.; Kunz, Robert F.: A multiphase level-set approach for all-Mach numbers (2018)

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