MPDATA swMATH ID: 596 Software Authors: Smolarkiewicz, Piotr K.; Margolin, Len G. Description: MPDATA: A finite-difference solver for geophysical flows. This article is a review of MPDATA, a class of methods for numerical simulation of fluid flows based on sign-preserving properties of upstream differencing. MPDATA was designed originally as an inexpensive alternative to flux-limited schemes for evaluating the advection of nonnegative thermodynamic variables (such as liquid water or water vapour) in atmospheric models. During the last decade, MPDATA has evolved from a simple advection scheme to a general approach for integrating the conservation laws of geophysical fluids on micro-to-planetary scales. The purpose of this paper is to summarize the basic concepts leading to a family of MPDATA schemes, to review existing MPDATA options, and to demonstrate the use of MPDATA to effectively construct two distinct types of models (elastic and anelastic) for complex geophysical flows. \(copyright\) Academic Press Homepage: http://rd.springer.com/chapter/10.1007%2F978-1-4615-0663-8_81 Keywords: nonoscillatory scheme; MPDATA; sign-preserving properties; upstream differencing; advection scheme; conservation laws Related Software: EULAG; NICAM; libmpdata++; HE-E1GODF; chammp; CASTRO; MAESTRO; VisIt; ICON; COSMO-EULAG; SHASTA; Atlas; OpenCoarrays; CoArray; MATLAB expm; MPAS-Ocean; OpenCourseWare; MPI; Expokit; Spalart-Allmaras Cited in: 78 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year MPDATA: third-order accuracy for variable flows. Zbl 1384.86008Waruszewski, Maciej; Kühnlein, Christian; Pawlowska, Hanna; Smolarkiewicz, Piotr K. 2018 MPDATA – a multipass donor cell solver for geophysical flows. Zbl 1064.86500Smolarkiewicz, P. K.; Margolin, L. G. 2001 all top 5 Cited by 98 Authors 33 Smolarkiewicz, Piotr K. 16 Szmelter, Joanna 12 Margolin, Len G. 7 Kühnlein, Christian 4 Edwards, Michael G. 4 Shashkov, Mikhail J. 3 Adams, Nikolaus A. 3 Domaradzki, J. Andrzej 3 Gillard, Mike 3 Hickel, Stefan 3 Lamine, Sadok 3 Prusa, Joseph M. 3 Rider, William J. 3 Wedi, Nils P. 3 Wyszogrodzki, Andrzej A. 2 Almgren, Ann S. 2 Bell, John B. 2 Garcia-Navarro, Pilar 2 Higdon, Robert L. 2 Hill, Ryan N. 2 May, Sandra 2 Nonaka, Andy 2 Zhang, Zhao 1 Ahmad, Nash’at N. 1 Akimenko, Vitalii V. 1 Arabas, Sylwester 1 Bacon, David P. 1 Bai, Junqiang 1 Benacchio, Tommaso 1 Botchorishvili, Ramaz 1 Bowker, George 1 Brentnall, Stuart J. 1 Cao, Zhixin 1 Claisse, Alexandra 1 Cocetta, Francesco 1 Davies, Terry 1 Davis, Robert H. 1 Deconinck, Willem 1 Després, Bruno 1 Diamessis, Peter J. 1 Dimotakis, Paul E. 1 Dörnbrack, Andreas 1 Drikakis, Dimitris 1 Farhat, Ahmad 1 Franz, Sebastian 1 Gissinger, Jacob R. 1 Grabowski, Wojciech W. 1 Gunzburger, Max D. 1 Gutowski, W. J. 1 Hall, Mary S. 1 Hamrud, Mats 1 Heist, David 1 Hubbard, Matthew E. 1 Jarecka, Dorota 1 Jaruga, Anna 1 Jones, Don A. 1 Ju, Lili 1 Kempe, Tobias 1 Klein, Rupert 1 Labourasse, Emmanuel 1 Lan, Rihui 1 Ledoux, Franck 1 Leng, Wei 1 Malinowski, Szymon P. 1 Matheou, Georgios 1 Methven, John 1 Mozdzynski, George 1 Nakonechny, A. G. 1 Ortiz, Pablo 1 Pawlowska, Hanna 1 Perry, Steven G. 1 Piotrowski, Zbigniew P. 1 Pironneau, Olivier 1 Plesko, Catherine 1 Poje, Andrew C. 1 Qu, Feng 1 Richards, Kelvin J. 1 Saidi, Mohammad Said 1 Sani, Modiah 1 Sarma, Ananthakrishna 1 Schranner, Felix S. 1 Sharman, Robert 1 Shaw, James R. 1 Shen, Jie 1 Sopta, Luka 1 Sorbjan, Zbigniew 1 Subich, Christopher J. 1 Sun, Di 1 Tachim Medjo, Theodore 1 Vuković, Senka 1 Wang, Shouhong 1 Wang, Zhu 1 Waruszewski, Maciej 1 Weil, Jeffrey C. 1 Weller, Hilary 1 Winter, C. Larrabee 1 Xiao, Feng 1 Zinchenko, Alexander Z. all top 5 Cited in 16 Serials 38 Journal of Computational Physics 13 International Journal for Numerical Methods in Fluids 6 Computers and Fluids 5 Computer Methods in Applied Mechanics and Engineering 3 SIAM Journal on Scientific Computing 2 Theoretical and Computational Fluid Dynamics 1 Computers & Mathematics with Applications 1 Journal of Fluid Mechanics 1 Fluid Dynamics Research 1 Journal of Computational and Applied Mathematics 1 Physica D 1 Cybernetics and Systems Analysis 1 Communications in Applied Mathematics and Computational Science 1 Scientia Iranica. Transaction B: Mechanical Engineering 1 Journal of Theoretical Biology 1 Evolution Equations and Control Theory all top 5 Cited in 11 Fields 63 Fluid mechanics (76-XX) 42 Numerical analysis (65-XX) 25 Geophysics (86-XX) 12 Partial differential equations (35-XX) 3 Mechanics of deformable solids (74-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Biology and other natural sciences (92-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year