The multidimensional positive definite advection transport algorithm: nonoscillatory option

Smolarkiewicz, Piotr K.; Grabowski, Wojciech W.

doi:10.1016/0021-9991(90)90105-a

Cited by 332 publications

(233 citation statements)

References 18 publications

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“…The model o ers a variety of advection schemes, from the most simple second-order, centred scheme to the sophisticated MPDATA scheme of Smolarkiewicz and Grabowski (1990). We will hereafter describe a simple Multidimensional Positive De®nite Centred Di erence Scheme (MPDCD) recently developed, that appears to provide a particularly interesting quality-cost ratio.…”

Section: Positive De®nite Advection Schemementioning

confidence: 99%

The Meso-NH Atmospheric Simulation System. Part I: adiabatic formulation and control simulations

et al. 1998

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Abstract. The Meso-NH Atmospheric Simulation System is a joint e ort of the Centre National de Recherches MeÂ teÂ orologiques and Laboratoire d'AeÂ rologie. It comprises several elements; a numerical model able to simulate the atmospheric motions, ranging from the large meso-alpha scale down to the micro-scale, with a comprehensive physical package, a¯exible ®le manager, an ensemble of facilities to prepare initial states, either idealized or interpolated from meteorological analyses or forecasts, a¯exible post-processing and graphical facility to visualize the results, and an ensemble of interactive procedures to control these functions. Some of the distinctive features of this ensemble are the following: the model is currently based on the Lipps and Hemler form of the anelastic system, but may evolve towards a more accurate form of the equations system. In the future, it will allow for simultaneous simulation of several scales of motion, by the so-called``interactive grid-nesting technique''. It allows for the in-line computation and accumulation of various terms of the budget of several quantities. It allows for the transport and di usion of passive scalars, to be coupled with a chemical module. It uses the relatively new Fortran 90 compiler. It is tailored to be easily implemented on any UNIX machine. Meso-NH is designed as a research tool for small and meso-scale atmospheric processes. It is freely accessible to the research community, and we have tried to make it as``user-friendly'' as possible, and as general as possible, although these two goals sometimes appear contradictory. The present paper presents a general description of the adiabatic formulation and some of the basic validation simulations. A list of the currently available physical parametrizations and initialization methods is also given. A more precise description of these aspects will be provided in a further paper.

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Section: Positive De®nite Advection Schemementioning

confidence: 99%

The Meso-NH Atmospheric Simulation System. Part I: adiabatic formulation and control simulations

et al. 1998

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“…[11] The multidimensional positive definite advection transport algorithm (MPDATA) [Smolarkiewicz, 1984;Smolarkiewicz and Clark, 1986;Smolarkiewicz and Grabowski, 1990] is utilized in the advection scheme. No additional horizontal diffusivity is needed for this resolution.…”

Section: Model Configurationmentioning

confidence: 99%

Numerical study of the diapycnal flow through a tidal front with passive tracers

Houghton

Chen

et al. 2004

J. Geophys. Res.

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[1] A two-dimensional numerical model is used to study the diapycnal flow through a tidal front with passive tracers. In a basic numerical experiment a passive tracer is released into the bottom water at the offshore edge of a tidal front, and it subsequently moves on-bank with a velocity that decreases with time. This qualitatively agrees with a recent field experiment using a dye tracer on Georges Bank. Additional experiments are performed to investigate the sensitivity of the tracer dispersion to the tidal phase and the location of tracer release within the front. As the release point is moved on-bank across the front, the tracer velocity decreases until it weakly reverses on the on-bank edge of the front. This trend can be understood by considering the structure of the Lagrangian velocity field in the tidal front, the degree of vertical mixing of the tracer, and the concentrationweighted mean patch velocity. The tidal phase at the time of tracer release does not significantly affect the tracer dispersion.

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“…This bene®ts signi®cantly the overall accuracy of the resulting FCT scheme (see Fig. 5 in [43] and the accompanying discussion).…”

Section: Homogeneous Transport Rmentioning

confidence: 91%

“…scheme (in the sense of FCT) [43]. More recently, MPDATA has been generalized for systems of equations with arbitrary forcing [41,42].…”

Section: Introductory Remarksmentioning

confidence: 99%

A discrete operator calculus for finite difference approximations

Margolin

2000

Computer Methods in Applied Mechanics and Engineering

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In this article we describe two areas of recent progress in the construction of accurate and robust ®nite di erence algorithms for continuum dynamics. The support operators method (SOM) provides a conceptual framework for deriving a discrete operator calculus, based on mimicking selected properties of the di erential operators. In this paper, we choose to preserve the fundamental conservation laws of a continuum in the discretization. A strength of SOM is its applicability to irregular unstructured meshes. We describe the construction of an operator calculus suitable for gas dynamics and for solid dynamics, derive general formulae for the operators, and exhibit their realization in 2D cylindrical coordinates. The multidimensional positive de®nite advection transport algorithm (MPDATA) provides a framework for constructing accurate nonoscillatory advection schemes. In particular, the nonoscillatory property is important in the remapping stage of arbitrary-Lagrangian±Eulerian (ALE) programs. MPDATA is based on the sign-preserving property of upstream di erencing, and is fully multidimensional. We describe the basic second-order-accurate method, and review its generalizations. We show examples of the application of MPDATA to an advection problem, and also to a complex¯uid ow. We also provide an example to demonstrate the blending of the SOM and MPDATA approaches. Ó

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The multidimensional positive definite advection transport algorithm: nonoscillatory option

Cited by 332 publications

References 18 publications

The Meso-NH Atmospheric Simulation System. Part I: adiabatic formulation and control simulations

The Meso-NH Atmospheric Simulation System. Part I: adiabatic formulation and control simulations

Numerical study of the diapycnal flow through a tidal front with passive tracers

A discrete operator calculus for finite difference approximations

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