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

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  1. Arabas, Sylwester; Farhat, Ahmad: Derivative pricing as a transport problem: MPDATA solutions to Black-Scholes-type equations (2020)
  2. Szmelter, Joanna; Gillard, Mike: A multidimensional positive definite remapping algorithm for unstructured meshes (2020)
  3. Gissinger, Jacob R.; Zinchenko, Alexander Z.; Davis, Robert H.: Drops with insoluble surfactant squeezing through interparticle constrictions (2019)
  4. Margolin, Len; Plesko, Catherine: Discrete regularization (2019)
  5. Smolarkiewicz, Piotr K.; Kühnlein, Christian; Wedi, Nils P.: Semi-implicit integrations of perturbation equations for all-scale atmospheric dynamics (2019)
  6. Szmelter, Joanna; Smolarkiewicz, Piotr K.; Zhang, Zhao; Cao, Zhixin: Non-oscillatory forward-in-time integrators for viscous incompressible flows past a sphere (2019)
  7. Subich, Christopher J.: Higher-order finite volume differential operators with selective upwinding on the icosahedral spherical grid (2018)
  8. Waruszewski, Maciej; Kühnlein, Christian; Pawlowska, Hanna; Smolarkiewicz, Piotr K.: MPDATA: third-order accuracy for variable flows (2018)
  9. Kühnlein, Christian; Smolarkiewicz, Piotr K.: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics (2017)
  10. Shaw, James; Weller, Hilary; Methven, John; Davies, Terry: Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes (2017)
  11. Smolarkiewicz, Piotr K.; Kühnlein, Christian; Grabowski, Wojciech W.: A finite-volume module for cloud-resolving simulations of global atmospheric flows (2017)
  12. Matheou, Georgios; Dimotakis, Paul E.: Scalar excursions in large-eddy simulations (2016)
  13. 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)
  14. Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng: Simulation of all-scale atmospheric dynamics on unstructured meshes (2016)
  15. Jarecka, Dorota; Jaruga, Anna; Smolarkiewicz, Piotr K.: A spreading drop of shallow water (2015)
  16. Lamine, Sadok; Edwards, Michael G.: Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids (2015)
  17. Schranner, Felix S.; Domaradzki, J. Andrzej; Hickel, Stefan; Adams, Nikolaus A.: Assessing the numerical dissipation rate and viscosity in numerical simulations of fluid flows (2015)
  18. Szmelter, Joanna; Zhang, Zhao; Smolarkiewicz, Piotr K.: An unstructured-mesh atmospheric model for nonhydrostatic dynamics: towards optimal mesh resolution (2015)
  19. Smolarkiewicz, Piotr K.; Kühnlein, Christian; Wedi, Nils P.: A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics (2014)
  20. Lamine, Sadok; Edwards, Michael G.: Higher order cell-based multidimensional upwind schemes for flow in porous media on unstructured grids (2013)

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