Abstract
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.
Keywords
- 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.
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References
Godunov S K (1959). Finite Difference Methods for Numerical Computations of Discontinuous Solutions of Equations of Fluid Dynamics. Mat. Sb. 47, pp 271–306.
Margolin L G and Smolarkiewicz P K (1998). Antidiífusive Velocities for Multipass Donor Cell Advection. SIAM J. Sci. Comput. 20, pp 907–929.
Margolin L G, Smolarkiewicz P K and Sorbjan Z (1999). Large-eddy Simulations of Convective Boundary Layers Using Nonoscillatory Differencing. Physica D133, pp 390–397.
Smolarkiewicz P K (1983). A Simple Positive Definite Advection Scheme with Small Implicit Diffusion. Mon. Wea. Rev. 111, pp 479–486.
Smolarkiewicz P K (1984). A Fully Multidimensional Positive Definite Advection Transport Algorithm with Small Implicit Diffusion. J. Comput. Phys. 54, pp 325–362.
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 Special35, pp 127–152.
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.
Smolarkiewicz P K and Margolin L G (1998). MPDATA: A Finite-Difference Solver For Geophysical Flows. J. Comput. Phys. 140, pp 459–480.
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.
Strang G (1968). On the Construction and Comparison of Difference Schemes. SIAM J. Numer. Anal. 5, pp 506–517.
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© 2001 Springer Science+Business Media New York
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Smolarkiewicz, P.K., Margolin, L.G. (2001). MPDATA-A Multipass Donor Cell Solver for Geophysical Flows. In: Toro, E.F. (eds) Godunov Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-0663-8_81
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DOI: https://doi.org/10.1007/978-1-4615-0663-8_81
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-5183-2
Online ISBN: 978-1-4615-0663-8
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