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In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...
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Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature difference, heat transfer occurs. It may occur rapidly, such as through a cooking pan, or slowly, such as through the walls of a picnic ice box. So many processes involve heat transfer that it is hard to imagine a situation where no heat transfer occurs. Yet, every heat transfer takes place by only three methods: conduction, convection, and radiation.
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Advection modes by optimal mass transfer.

Angelo Iollo1, Damiano Lombardi2

  • 1Institut de Mathématiques de Bordeaux, UMR 5251 CNRS, Université de Bordeaux, Inria Bordeaux, Sud Ouest, 33400 Talence, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

This study introduces a novel method for low-order advection representation using mass transfer problems. This approach offers an effective alternative to traditional global modes for advection-dominated physical models.

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Area of Science:

  • Computational physics
  • Applied mathematics
  • Fluid dynamics

Background:

  • Classical model reduction uses global modes (e.g., principal component analysis) for approximating physical models.
  • Global modes are effective for stability and accuracy but can be limited for advection-dominated systems, resembling Fourier expansions.

Purpose of the Study:

  • To develop a new method for low-order representation of advection.
  • To address limitations of global modes in capturing advection phenomena accurately.

Main Methods:

  • The proposed method determines a low-order representation of advection.
  • It is based on solving Monge-Kantorovich mass transfer problems.

Main Results:

  • The method provides an effective low-order representation for advection.
  • Applications demonstrated success in point vortex scattering, Korteweg-de Vries equation, and hurricane Dean advection.

Conclusions:

  • The Monge-Kantorovich mass transfer approach offers a powerful alternative for advection modeling.
  • This technique enhances the accuracy and efficiency of reduced-order models in advection-dominated scenarios.