MPDATA-A Multipass Donor Cell Solver for Geophysical Flows

  • P. K. Smolarkiewicz
  • L. G. Margolin


This article is a summary of MPDATA, a class of methods for the numerical simulation of fluid flows based on the 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 vapor) 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 outline the basic concepts leading to a family of MPDATA schemes, highlight existing MPDATA options, and to comment on the use of MPDATA to model complex geophysical flows.


Large Eddy Simulation Donor Cell Truncation Error Convective Boundary Layer Advection Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Godunov S K (1959). Finite Difference Methods for Numerical Computations of Discontinuous Solutions of Equations of Fluid Dynamics. Mat. Sb. 47, pp 271–306.MathSciNetGoogle Scholar
  2. Margolin L G and Smolarkiewicz P K (1998). Antidiífusive Velocities for Multipass Donor Cell Advection. SIAM J. Sci. Comput. 20, pp 907–929.MathSciNetCrossRefGoogle Scholar
  3. Margolin L G, Smolarkiewicz P K and Sorbjan Z (1999). Large-eddy Simulations of Convective Boundary Layers Using Nonoscillatory Differencing. Physica D 133, pp 390–397.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Smolarkiewicz P K (1983). A Simple Positive Definite Advection Scheme with Small Implicit Diffusion. Mon. Wea. Rev. 111, pp 479–486.CrossRefGoogle Scholar
  5. Smolarkiewicz P K (1984). A Fully Multidimensional Positive Definite Advection Transport Algorithm with Small Implicit Diffusion. J. Comput. Phys. 54, pp 325–362.CrossRefGoogle Scholar
  6. Smolarkiewicz P K and Margolin L G (1997). On Forward-in-Time Differencing for Fluids: An Eulerian/Semi-Lagrangian Nonhydrostatic Model for Stratified Flows. Atmos. Ocean Special 35, pp 127–152.CrossRefGoogle Scholar
  7. Smolarkiewicz P K, Grubišič V and Margolin L G (1998). Forward-in-Time Differencing for Fluids: Nonhydrostatic Modeling of Rotating Stratified Flows on a Mountainous Sphere. Numerical Methods for Fluid Dynamics VI, pp 507–513. Baines M J (Editor), Will Print, Oxford.Google Scholar
  8. Smolarkiewicz P K and Margolin L G (1998). MPDATA: A Finite-Difference Solver For Geophysical Flows. J. Comput. Phys. 140, pp 459–480.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Smolarkiewicz P K, Grubišić V, Margolin L G and Wyszogrodzki A A (1999) Forward-in-Time Differencing for Fluids: Nonhydrostatic Modeling of Fluid Motions on a Sphere. Recent Developments in Numerical Methods for Atmospheric Modelling, pp 21–43. ECMWF, Reading, UK.Google Scholar
  10. Strang G (1968). On the Construction and Comparison of Difference Schemes. SIAM J. Numer. Anal. 5, pp 506–517.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • P. K. Smolarkiewicz
    • 1
  • L. G. Margolin
    • 2
  1. 1.National Center for Atmospheric ResearchBoulderUSA
  2. 2.Los Alamos National LaboratoryLos AlamosUSA

Personalised recommendations