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. Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F.: Exploring various flux vector splittings for the magnetohydrodynamic system (2016)
  2. Ciobanu, Oana; Halpern, Laurence; Juvigny, Xavier; Ryan, Juliette: Overlapping domain decomposition applied to the Navier-Stokes equations (2016)
  3. 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)
  4. 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)
  5. Morin, Alexandre; Flåtten, Tore: A two-fluid four-equation model with instantaneous thermodynamical equilibrium (2016)
  6. Berthelin, Florent; Goudon, Thierry; Minjeaud, Sebastian: Kinetic schemes on staggered grids for barotropic Euler models: entropy-stability analysis (2015)
  7. Choi, Jung J.: Hybrid spectral difference/embedded finite volume method for conservation laws (2015)
  8. Maruthi, N.H.; Raghurama Rao, S.V.: An entropy stable central solver for Euler equations (2015)
  9. Moguen, Yann; Bruel, Pascal; Dick, Erik: Solving low Mach number Riemann problems by a momentum interpolation method (2015)
  10. Moguen, Yann; Delmas, Simon; Perrier, Vincent; Bruel, Pascal; Dick, Erik: Godunov-type schemes with an inertia term for unsteady full Mach number range flow calculations (2015)
  11. Xu, Kun: Direct modeling for computational fluid dynamics. Construction and application of unified gas-kinetic schemes (2015)
  12. Ben Nasr, N.; Gerolymos, G.A.; Vallet, I.: Low-diffusion approximate Riemann solvers for Reynolds-stress transport (2014)
  13. Cheng, Juan; Shu, Chi-Wang: Positivity-preserving Lagrangian scheme for multi-material compressible flow (2014)
  14. Han, L.H.; Hu, X.Y.; Adams, N.A.: Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure (2014)
  15. Kriel, A.J.: A flux splitting method for the Euler equations (2014)
  16. Nonomura, Taku; Kitamura, Keiichi; Fujii, Kozo: A simple interface sharpening technique with a hyperbolic tangent function applied to compressible two-fluid modeling (2014)
  17. 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)
  18. Rinaldi, Enrico; Pecnik, Rene; Colonna, Piero: Exact Jacobians for implicit Navier-Stokes simulations of equilibrium real gas flows (2014)
  19. Zhang, Bin; Liu, Hong; Chen, Fang; Wang, Jian Hang: The equilibrium state method for hyperbolic conservation laws with stiff reaction terms (2014)
  20. Chang, Chih-Hao; Deng, Xiaolong; Theofanous, Theo G.: Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method (2013)

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