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. Deng, Xiao-Long; Li, Maojun: Simulating compressible two-medium flows with sharp-interface adaptive Runge-Kutta discontinuous Galerkin methods (2018)
  2. Peles, Oren; Turkel, Eli: Acceleration methods for multi-physics compressible flow (2018)
  3. Couderc, F.; Duran, A.; Vila, J.-P.: An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification (2017)
  4. Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.: A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension (2017)
  5. Gerlinger, Peter: Lagrangian transported MDF methods for compressible high speed flows (2017)
  6. Kitamura, Keiichi; Hashimoto, Atsushi: Simple a posteriori slope limiter (post limiter) for high resolution and efficient flow computations (2017)
  7. Rodionov, Alexander V.: Artificial viscosity in Godunov-type schemes to cure the carbuncle phenomenon (2017)
  8. Shen, Hua; Wen, Chih-Yung; Parsani, Matteo; Shu, Chi-Wang: Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids (2017)
  9. Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.: Scalar conservation and boundedness in simulations of compressible flow (2017)
  10. Xie, Bin; Deng, Xi; Sun, Ziyao; Xiao, Feng: A hybrid pressure-density-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method (2017)
  11. Xie, Wenjia; Li, Wei; Li, Hua; Tian, Zhengyu; Pan, Sha: On numerical instabilities of Godunov-type schemes for strong shocks (2017)
  12. Alvarez Laguna, A.; Lani, A.; Deconinck, H.; Mansour, N.N.; Poedts, S.: A fully-implicit finite-volume method for multi-fluid reactive and collisional magnetized plasmas on unstructured meshes (2016)
  13. Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F.: Exploring various flux vector splittings for the magnetohydrodynamic system (2016)
  14. Chen, Yibing; Jiang, Song; Liu, Na: HFVS: an arbitrary high order approach based on flux vector splitting (2016)
  15. Ciobanu, Oana; Halpern, Laurence; Juvigny, Xavier; Ryan, Juliette: Overlapping domain decomposition applied to the Navier-Stokes equations (2016)
  16. 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)
  17. Dellacherie, S.; Jung, J.; Omnes, P.; Raviart, P.-A.: Construction of modified Godunov-type schemes accurate at any Mach number for the compressible Euler system (2016)
  18. Fraysse, F.; Redondo, C.; Rubio, G.; Valero, E.: Upwind methods for the Baer-Nunziato equations and higher-order reconstruction using artificial viscosity (2016)
  19. Houim, Ryan W.; Oran, Elaine S.: A multiphase model for compressible granular-gaseous flows: formulation and initial tests (2016)
  20. Kawashima, Rei; Komurasaki, Kimiya; Schönherr, Tony: A flux-splitting method for hyperbolic-equation system of magnetized electron fluids in quasi-neutral plasmas (2016)

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