## AUSM

 swMATH ID: 6367 Software Authors: MS Liou; Ullrich, Paul A.; Jablonowski, Christiane Description: 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. Homepage: http://www.sciencedirect.com/science/article/pii/S0021999196902569 Keywords: Riemann solver Related Software: HLLE; HE-E1GODF; AUSMPW+; Spalart-Allmaras; FLICA-OVAP; RIEMANN; PETSc; HLLC; L2Roe; CATHARE; CHEMKIN; OpenFOAM; elsA; CANS+; Athena; FaSTAR; CUDA; MOOD; PARAMESH; chammp Referenced in: 326 Publications
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### Referenced by 591 Authors

 15 Kitamura, Keiichi 8 Deck, Sebastien 8 Evje, Steinar 8 Liou, Meng-Sing 7 Dick, Erik 7 Flåtten, Tore 7 Moguen, Yann 7 Niu, Yang-Yao 7 Quinlan, Nathan J. 7 Yan, Chao 6 Bruel, Pascal 6 Chang, Chih-Hao 6 Chen, Shusheng 6 Deng, Xiaolong 6 Qu, Feng 6 Sun, Di 6 Weiss, Pierre-élie 5 Billet, Germain 5 Li, Hua 5 Li, Xuesong 5 Schneider, Kai 5 Tian, Zhengyu 4 Adams, Nikolaus A. 4 Bai, Junqiang 4 Domingues, Margarete O. 4 Edwards, Jack R. 4 Gomes, Sônia Maria 4 Nonomura, Taku 4 Toro, Eleuterio Francisco 4 Xie, Wenjia 3 Chassaing, Jean-Camille 3 Corre, Christophe 3 De, Sudipta 3 Dellacherie, Stéphane 3 Fjelde, Kjell Kåre 3 Freund, Jonathan B. 3 Goncalves, Eric 3 Gu, Chunwei 3 Herbin, Raphaèle 3 Jiang, Lingjie 3 Kapen, Pascalin Tiam 3 Kim, Chongam 3 Latché, Jean-Claude 3 Lien, Fue-Sang 3 Lin, Boxi 3 Moghimi, Mohsen H. 3 Munkejord, Svend Tollak 3 Paillère, Henri 3 Pandare, Aditya K. 3 Pantano, Carlos 3 Roussel, Olivier 3 Sagaut, Pierre 3 Shima, Eiji 3 Shu, Chi-Wang 3 Terashima, Hiroshi 3 Zhang, Fan 3 Zhang, Ye 2 Alvarez Laguna, A. 2 Avellan, François 2 Azevedo, João Luiz F. 2 Beneš, Luděk 2 Bocharov, A. N. 2 Bugeat, B. 2 Cascales, J. R. García 2 Chen, Biaosong 2 Clerc, Sébastien 2 Colonna, Piero 2 Deng, Xi 2 Desjardin, Paul E. 2 Ding, Hang 2 Fraysse, François 2 Fu, Song 2 Fujii, Kozo 2 Fürst, Jiří 2 Gao, Zhenghong 2 Gerlinger, Peter 2 Ghislain, Tchuen 2 Goudon, Thierry 2 Hashimoto, Atsushi 2 Hérard, Jean-Marc 2 Houim, Ryan W. 2 Jablonowski, Christiane 2 Jahanbakhsh, Ebrahim 2 John, Bibin 2 Kawashima, Rei 2 Kim, Kyuhong 2 Komurasaki, Kimiya 2 Kousksou, Tarik 2 Kulkarni, Vinayak S. 2 Kundu, Abhishek 2 Lani, Andrea 2 Li, Maojun 2 Li, Zhiyong 2 Liu, Jun 2 Liu, Qingsong 2 Luo, Hong 2 Lyra, Paulo Roberto Maciel 2 Maertens, Audrey P. 2 Magin, Thierry E. 2 Mamashita, Tomohiro ...and 491 more Authors
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### Referenced in 50 Serials

 122 Journal of Computational Physics 83 Computers and Fluids 13 International Journal of Computational Fluid Dynamics 10 Journal of Fluid Mechanics 9 Communications in Computational Physics 7 International Journal for Numerical Methods in Fluids 5 Applied Mathematics and Mechanics. (English Edition) 4 Computers & Mathematics with Applications 4 Computer Methods in Applied Mechanics and Engineering 4 SIAM Journal on Scientific Computing 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Shock Waves 3 Applied Mathematics and Computation 3 Flow, Turbulence and Combustion 2 Computer Physics Communications 2 Mathematics and Computers in Simulation 2 Engineering Analysis with Boundary Elements 2 Mathematical Problems in Engineering 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 European Journal of Mechanics. B. Fluids 2 Combustion Theory and Modelling 2 Matematicheskoe Modelirovanie 2 Archives of Computational Methods in Engineering 2 International Journal of Computational Methods 2 Advances in Applied Mathematics and Mechanics 1 Fluid Dynamics 1 Wave Motion 1 Mathematics of Computation 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Computational Mathematics and Mathematical Physics 1 Applied Mathematical Modelling 1 SIAM Journal on Mathematical Analysis 1 Journal of Applied Mechanics and Technical Physics 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Comptes Rendus. Mécanique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Progress in Computational Fluid Dynamics 1 Acta Mechanica Sinica 1 Mathematical Modelling of Natural Phenomena 1 International Journal of Advances in Engineering Sciences and Applied Mathematics 1 Journal of the Korean Society for Industrial and Applied Mathematics 1 Advances in Computational Fluid Dynamics 1 Journal of Computational Methods in Physics 1 International Journal of Applied and Computational Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition)
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### Referenced in 11 Fields

 312 Fluid mechanics (76-XX) 147 Numerical analysis (65-XX) 42 Partial differential equations (35-XX) 17 Classical thermodynamics, heat transfer (80-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Mechanics of deformable solids (74-XX) 2 Computer science (68-XX) 2 Geophysics (86-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Operations research, mathematical programming (90-XX)