MPDATA

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


References in zbMATH (referenced in 64 articles , 2 standard articles )

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  1. Waruszewski, Maciej; Kühnlein, Christian; Pawlowska, Hanna; Smolarkiewicz, Piotr K.: MPDATA: third-order accuracy for variable flows (2018)
  2. Kühnlein, Christian; Smolarkiewicz, Piotr K.: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics (2017)
  3. Shaw, James; Weller, Hilary; Methven, John; Davies, Terry: Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes (2017)
  4. Smolarkiewicz, Piotr K.; Kühnlein, Christian; Grabowski, Wojciech W.: A finite-volume module for cloud-resolving simulations of global atmospheric flows (2017)
  5. Matheou, Georgios; Dimotakis, Paul E.: Scalar excursions in large-eddy simulations (2016)
  6. Smolarkiewicz, Piotr K.; Deconinck, Willem; Hamrud, Mats; Kühnlein, Christian; Mozdzynski, George; Szmelter, Joanna; Wedi, Nils P.: A finite-volume module for simulating global all-scale atmospheric flows (2016)
  7. Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng: Simulation of all-scale atmospheric dynamics on unstructured meshes (2016)
  8. Jarecka, Dorota; Jaruga, Anna; Smolarkiewicz, Piotr K.: A spreading drop of shallow water (2015)
  9. Szmelter, Joanna; Zhang, Zhao; Smolarkiewicz, Piotr K.: An unstructured-mesh atmospheric model for nonhydrostatic dynamics: towards optimal mesh resolution (2015)
  10. Smolarkiewicz, Piotr K.; Kühnlein, Christian; Wedi, Nils P.: A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics (2014)
  11. Lamine, Sadok; Edwards, Michael G.: Higher order cell-based multidimensional upwind schemes for flow in porous media on unstructured grids (2013)
  12. Smolarkiewicz, Piotr K.; Szmelter, Joanna; Wyszogrodzki, Andrzej A.: An unstructured-mesh atmospheric model for nonhydrostatic dynamics (2013)
  13. Claisse, A.; Després, B.; Labourasse, E.; Ledoux, F.: A new exceptional points method with application to cell-centered Lagrangian schemes and curved meshes (2012)
  14. Kühnlein, Christian; Smolarkiewicz, Piotr K.; Dörnbrack, Andreas: Modelling atmospheric flows with adaptive moving meshes (2012)
  15. Edwards, Michael G.: Multi-dimensional wave-oriented upwind schemes with reduced cross-wind diffusion for flow in porous media (2011)
  16. Hill, Ryan N.; Szmelter, Joanna: A multidimensional positive definite remapping for Lagrangian solutions of the Noh problem (2011)
  17. Hill, Ryan N.; Szmelter, Joanna: A multidimensional positive definite remapping algorithm for arbitrary Lagrangian -- Eulerian methods (2011)
  18. May, Sandra; Nonaka, Andrew; Almgren, Ann; Bell, John: An unsplit, higher-order Godunov method using quadratic reconstruction for advection in two dimensions (2011)
  19. Nonaka, A.; May, S.; Almgren, A. S.; Bell, J. B.: A three-dimensional, unsplit Godunov method for scalar conservation laws (2011)
  20. Szmelter, Joanna; Smolarkiewicz, Piotr K.: An edge-based unstructured mesh framework for atmospheric flows (2011)

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