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. Ciobanu, Oana; Halpern, Laurence; Juvigny, Xavier; Ryan, Juliette: Overlapping domain decomposition applied to the Navier-Stokes equations (2016)
  2. Deiterding, Ralf; Domingues, Margarete O.; Gomes, S^onia M.; Schneider, Kai: Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible Euler equations (2016)
  3. Morin, Alexandre; Flåtten, Tore: A two-fluid four-equation model with instantaneous thermodynamical equilibrium (2016)
  4. Berthelin, Florent; Goudon, Thierry; Minjeaud, Sebastian: Kinetic schemes on staggered grids for barotropic Euler models: entropy-stability analysis (2015)
  5. Maruthi, N.H.; Raghurama Rao, S.V.: An entropy stable central solver for Euler equations (2015)
  6. Xu, Kun: Direct modeling for computational fluid dynamics. Construction and application of unified gas-kinetic schemes (2015)
  7. Quinlan, Nathan J.; Lobovský, Libor; Nestor, Ruairi M.: Development of the meshless finite volume particle method with exact and efficient calculation of interparticle area (2014)
  8. Chang, Chih-Hao; Deng, Xiaolong; Theofanous, Theo G.: Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method (2013)
  9. Herbin, R.; Latché, J.-C.; Nguyen, T.T.: Explicit staggered schemes for the compressible Euler equations (2013)
  10. Li, Xue-song; Gu, Chun-wei: Mechanism of Roe-type schemes for all-speed flows and its application (2013)
  11. Lockwood, Brian; Mavriplis, Dimitri: Gradient-based methods for uncertainty quantification in hypersonic flows (2013)
  12. Park, Jin Seok; Kim, Chongam: Extension of AUSMPW+ scheme for two-fluid model (2013)
  13. Robbins, D.J.; Cant, R.S.; Gladden, L.F.: Development of accurate, robust liquid equations of state for multi-phase CFD simulations with a modified AUSM$^+$-up scheme (2013)
  14. Soulat, Laurent; Ferrand, Pascal; Moreau, Stéphane; Aubert, Stéphane; Buisson, Martin: Efficient optimisation procedure for design problems in fluid mechanics (2013)
  15. Wang, Yong-Xian; Zhang, Li-Lun; Liu, Wei; Che, Yong-Gang; Xu, Chuan-Fu; Wang, Zheng-Hua; Zhuang, Yu: Efficient parallel implementation of large scale 3D structured grid CFD applications on the Tianhe-1A supercomputer (2013)
  16. Gerlinger, Peter: Multi-dimensional limiting for high-order schemes including turbulence and combustion (2012)
  17. Martínez Ferrer, Pedro José; Flåtten, Tore; Tollak Munkejord, Svend: On the effect of temperature and velocity relaxation in two-phase flow models (2012)
  18. Moguen, Yann; Kousksou, Tarik; Bruel, Pascal; Vierendeels, Jan; Dick, Erik: Pressure-velocity coupling allowing acoustic calculation in low Mach number flow (2012)
  19. Nonomura, Taku; Morizawa, Seiichiro; Terashima, Hiroshi; Obayashi, Shigeru; Fujii, Kozo: Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: Weighted compact nonlinear scheme (2012)
  20. Shen, Yiqing; Zha, Gecheng: Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier-Stokes equations (2012)

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