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; HLLC; PETSc; L2Roe; RIEMANN; CATHARE; CHEMKIN; OpenFOAM; elsA; CANS+; Athena; FaSTAR; CUDA; MOOD; PARAMESH; MUMPS Cited in: 337 Documents Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year MCore: a non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods. Zbl 1247.86007Ullrich, Paul A.; Jablonowski, Christiane 2012 A sequel to AUSM II: AUSM\(^+\)-up for all speeds. Zbl 1137.76344Liou, Meng-Sing 2006 all top 5 Cited by 637 Authors 15 Kitamura, Keiichi 8 Evje, Steinar 8 Liou, Meng-Sing 7 Deck, Sebastien 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 Hu, Xiangyu Y. 4 Nonomura, Taku 4 Toro, Eleuterio Francisco 4 Xie, Wenjia 3 Chassaing, Jean-Camille 3 Corre, Christophe 3 De, Sudipta 3 Dellacherie, Stéphane 3 Deng, Xi 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 Kundu, Abhishek 3 Lani, Andrea 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 Wang, Zhijian 3 Xie, Bin 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 Desjardin, Paul E. 2 Ding, Hang 2 Fraysse, François 2 Fu, Song 2 Fujii, Kozo 2 Fürst, Jiří 2 Gao, Haiyang 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 Li, Maojun 2 Li, Zhiyong 2 Liu, Jun 2 Liu, Qingsong 2 Liu, Yu 2 Luo, Hong ...and 537 more Authors all top 5 Cited in 51 Serials 126 Journal of Computational Physics 85 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 Computer Methods in Applied Mechanics and Engineering 5 Applied Mathematics and Mechanics. 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