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. 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)
  2. Deng, Xiao-Long; Li, Maojun: Simulating compressible two-medium flows with sharp-interface adaptive Runge-Kutta discontinuous Galerkin methods (2018)
  3. Fürst, Jiří: Development of a coupled matrix-free LU-SGS solver for turbulent compressible flows (2018)
  4. Gastaldo, Laura; Herbin, Raphaèle; Latché, Jean-Claude; Therme, Nicolas: A MUSCL-type segregated -- explicit staggered scheme for the Euler equations (2018)
  5. Kinzel, Michael P.; Lindau, Jules W.; Kunz, Robert F.: A multiphase level-set approach for all-Mach numbers (2018)
  6. Kitamura, Keiichi; Shima, Eiji: Pressure-equation-based SLAU2 for oscillation-free, supercritical flow simulations (2018)
  7. Li, Xuesong; Ren, Xiaodong; Gu, Chunwei: Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism (2018)
  8. Peles, Oren; Turkel, Eli: Acceleration methods for multi-physics compressible flow (2018)
  9. Couderc, F.; Duran, A.; Vila, J.-P.: An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification (2017)
  10. Gao, Song; Habashi, Wagdi G.; Isola, Dario; Baruzzi, Guido S.; Fossati, Marco: A Jacobian-free edge-based Galerkin formulation for compressible flows (2017)
  11. Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.: A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension (2017)
  12. Gerlinger, Peter: Lagrangian transported MDF methods for compressible high speed flows (2017)
  13. Haimovich, Ory; Frankel, Steven H.: Numerical simulations of compressible multicomponent and multiphase flow using a high-order targeted ENO (TENO) finite-volume method (2017)
  14. Kang, Xin; Gollan, Rowan J.; Jacobs, Peter A.; Veeraragavan, Ananthanarayanan: On the influence of modelling choices on combustion in narrow channels (2017)
  15. Kitamura, Keiichi; Hashimoto, Atsushi: Simple a posteriori slope limiter (post limiter) for high resolution and efficient flow computations (2017)
  16. Kundu, Abhishek; De, Sudipta: Navier-Stokes simulation of shock-heavy bubble interaction: comparison of upwind and WENO schemes (2017)
  17. Modesti, Davide; Pirozzoli, Sergio: A low-dissipative solver for turbulent compressible flows on unstructured meshes, with openfoam implementation (2017)
  18. Rodionov, Alexander V.: Artificial viscosity in Godunov-type schemes to cure the carbuncle phenomenon (2017)
  19. 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)
  20. Smirnov, N. N.; Nikitin, V. F.; Stamov, L. I.; Nerchenko, V. A.; Tyrenkova, V. V.: Numerical simulations of gaseous detonation propagation using different supercomputing architechtures (2017)

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