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


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  1. Lamine, Sadok; Edwards, Michael G.: Higher order cell-based multidimensional upwind schemes for flow in porous media on unstructured grids (2013)
  2. Claisse, A.; Després, B.; Labourasse, E.; Ledoux, F.: A new exceptional points method with application to cell-centered Lagrangian schemes and curved meshes (2012)
  3. Kühnlein, Christian; Smolarkiewicz, Piotr K.; Dörnbrack, Andreas: Modelling atmospheric flows with adaptive moving meshes (2012)
  4. Wyrzykowski, Roman; Rojek, Krzysztof; Szustak, Łukasz: Using Blue Gene/P and GPUs to accelerate computations in the EULAG model (2012)
  5. Hill, Ryan N.; Szmelter, Joanna: A multidimensional positive definite remapping for Lagrangian solutions of the Noh problem (2011)
  6. Hill, Ryan N.; Szmelter, Joanna: A multidimensional positive definite remapping algorithm for arbitrary Lagrangian -- Eulerian methods (2011)
  7. Nonaka, A.; May, S.; Almgren, A.S.; Bell, J.B.: A three-dimensional, unsplit Godunov method for scalar conservation laws (2011)
  8. Szmelter, Joanna; Smolarkiewicz, Piotr K.: An edge-based unstructured mesh framework for atmospheric flows (2011)
  9. Lamine, Sadok; Edwards, Michael G.: Higher order multidimensional upwind convection schemes for flow in porous media on structured and unstructured quadrilateral grids (2010)
  10. Saidi, M.S.; Sani, M.: Rayan: A polyhedral grid co-located incompressible finite volume solver. I: Basic design features (2010)
  11. Smolarkiewicz, Piotr K.; Winter, C.Larrabee: Pores resolving simulation of Darcy flows (2010)
  12. Szmelter, Joanna; Smolarkiewicz, Piotr K.: An edge-based unstructured mesh discretisation in geospherical framework (2010)
  13. Klein, Rupert: Asymptotics, structure, and integration of sound-proof atmospheric flow equations (2009)
  14. Piotrowski, Zbigniew P.; Smolarkiewicz, Piotr K.; Malinowski, Szymon P.; Wyszogrodzki, Andrzej A.: On numerical realizability of thermal convection (2009)
  15. Smolarkiewicz, Piotr K.; Szmelter, Joanna: Iterated upwind schemes for gas dynamics (2009)
  16. Diamessis, P.J.; Lin, Y.C.; Domaradzki, J.A.: Effective numerical viscosity in spectral multidomain penalty method-based simulations of localized turbulence (2008)
  17. Hickel, S.; Kempe, T.; Adams, N.A.: Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions (2008)
  18. Prusa, Joseph M.; Smolarkiewicz, Piotr K.; Wyszogrodzki, Andrzej A.: EULAG, a computational model for multiscale flows (2008)
  19. Smolarkiewicz, Piotr K.; Szmelter, Joanna: An MPDATA-based solver for compressible flows (2008)
  20. Smolarkiewicz, Piotr K.; Sharman, Robert; Weil, Jeffrey; Perry, Steven G.; Heist, David; Bowker, George: Building resolving large eddy simulations and comparison with wind tunnel experiments (2007)

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