chammp swMATH ID: 11655 Software Authors: Williamson, David L.; Drake, John B.; Hack, James J.; Jakob, Rüdiger; Swarztrauber, Paul N. Description: A standard test set for numerical approximations to the shallow water equations in spherical geometry. The numerical methods devised by the authors for solving shallow water equations in spherical geometry are applied to seven test cases presented in order of complexity. The aim, of course, is to perfect a numerical method for climate modelling. The seven cases are as follows: (i) advection of cosine bell over the pole, (ii) steady nonlinear zonal geostrophic flow, (iii) nonlinear steady zonal geostrophic flow with compact support, (iv) forced nonlinear system with a translating low pressure centre, (v) zonal flow over an isolated mountain, (vi) Rossby-Haurwitz wave, and (vii) observed atmospheric states. Homepage: http://www.netlib.org/chammp/index.html Keywords: climate modelling; advection; zonal geostrophic flow; translating low pressure centre; isolated mountain; Rossby-Haurwitz wave Related Software: PETSc; Firedrake; NICAM; MPAS-Ocean; phipm; Algorithm 919; HE-E1GODF; CAM3; AMATOS; UFL; COFFEE; TSFC; Matlab; SHASTA; DYNAMICO; Nektar++; Gmsh; AUSM; Slate; ICON Cited in: 177 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A standard test set for numerical approximations to the shallow water equations in spherical geometry. Zbl 0756.76060Williamson, David L.; Drake, John B.; Hack, James J.; Jakob, Rüdiger; Swarztrauber, Paul N. 1992 all top 5 Cited by 263 Authors 10 Giraldo, Francis X. 9 Cotter, Colin John 7 Nair, Ramachandran D. 6 Wright, Grady B. 6 Zerroukat, Mohamed 5 Cai, Xiao-Chuan 5 Flyer, Natasha 5 Pudykiewicz, Janusz A. 5 Yang, Chao 4 Chun, Sehun 4 Fornberg, Bengt 4 Korn, Peter 4 Lauritzen, Peter Hjort 4 Mehra, Mani 4 Peixoto, Pedro S. 4 Shashkin, Vladimir V. 4 Thuburn, John 4 Tomita, Hirofumi 3 Bauer, Werner 3 Behera, Ratikanta 3 Bendall, Thomas M. 3 Bonaventura, Luca 3 Chen, Qingshan 3 Cheong, Hyeong-Bin 3 Dethloff, Klaus 3 Erath, Christoph 3 Goyman, Gordey S. 3 Handorf, Dörthe 3 Iga, Shin-ichi 3 Jablonowski, Christiane 3 Ju, Lili 3 Läuter, Matthias 3 Lehto, Erik 3 Satoh, Masaki 3 Schreiber, Martin 3 Taylor, Mark Alan 3 Tolstykh, Mikhail A. 3 Ullrich, Paul Aaron 3 Wimmer, Golo A. 2 Behrens, Jorn 2 Blom, Joke G. 2 Bosler, Peter A. 2 Carfora, Maria Francesca 2 Chen, Chungang 2 Croisille, Jean-Pierre 2 Dubos, Thomas 2 Gaudreault, Stéphane 2 Gibson, Thomas H. 2 Goto, Koji 2 Guo, Ben-Yu 2 Hamon, François P. 2 Hoang, Thi-Thao-Phuong 2 Huang, Wei 2 Kevlahan, Nicholas K.-R. 2 Lanser, D. 2 Layton, Anita T. 2 LeFloch, Philippe Gerard 2 Marotzke, Jochem 2 Minion, Michael L. 2 Mittal, Rashmi 2 Peltier, W. R. 2 Rauser, Florian 2 Ringler, Todd D. 2 Rossmanith, James A. 2 Shankar, Varun 2 Shipton, Jemma 2 Smolarkiewicz, Piotr K. 2 Spotz, William F. 2 St-Cyr, Amik 2 Staniforth, Andrew Nigel 2 Stuhne, G. R. 2 Swarztrauber, Paul N. 2 Szmelter, Joanna 2 Tufo, Henry M. 2 Tumolo, Giovanni 2 Verwer, Jan G. 2 Wang, Zhu 2 Warburton, Timothy 2 Wood, Nigel B. 2 Xiao, Feng 2 Yang, Haijian 1 Aizinger, Vadym 1 Alonso, Beatriz 1 Alpert, Bradley K. 1 Amato, Umberto 1 Archibald, Rick 1 Arpaia, Luca 1 Baldauf, Michael 1 Bale, Derek S. 1 Bao, Lei 1 Barros, Saulo R. M. 1 Beale, J. Thomas 1 Beljadid, Abdelaziz 1 Ben-Artzi, Matania 1 Benito, Juan José 1 Bernard, Paul-Emile 1 Best, Meike 1 Betteridge, Jack 1 Bhumkar, Yogesh G. 1 Biagioli, Elisa ...and 163 more Authors all top 5 Cited in 29 Serials 114 Journal of Computational Physics 7 Applied Numerical Mathematics 6 Journal of Scientific Computing 6 SIAM Journal on Scientific Computing 4 Computers and Fluids 4 Computer Methods in Applied Mechanics and Engineering 3 Journal of Computational and Applied Mathematics 3 Numerische Mathematik 3 Applied Mathematical Modelling 3 Communications in Computational Physics 2 International Journal for Numerical Methods in Fluids 2 Applied Mathematics and Computation 2 Mathematics and Computers in Simulation 1 Computers & Mathematics with Applications 1 Geophysical and Astrophysical Fluid Dynamics 1 Journal of Engineering Mathematics 1 Mathematics of Computation 1 SIAM Journal on Numerical Analysis 1 Applied Mathematics and Mechanics. (English Edition) 1 Computational Mechanics 1 Mathematical and Computer Modelling 1 International Journal of Computer Mathematics 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Advances in Computational Mathematics 1 International Journal of Computational Fluid Dynamics 1 Computational Geosciences 1 Communications in Applied and Industrial Mathematics 1 SMAI Journal of Computational Mathematics all top 5 Cited in 17 Fields 124 Numerical analysis (65-XX) 120 Fluid mechanics (76-XX) 95 Geophysics (86-XX) 40 Partial differential equations (35-XX) 9 Global analysis, analysis on manifolds (58-XX) 3 Approximations and expansions (41-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year