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Tytuł artykułu

Numerical simulations of the humid atmosphere above a mountain

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Języki publikacji

EN

Abstrakty

EN
New avenues are explored for the numerical study of the two dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions for the system of equations. Flows above a mountain are classically treated by the so-called method of terrain following coordinate system. We avoid this discretization method which induces errors in the discretization of tangential derivatives near the topography. Instead we implement a first order finite volume method for the spatial discretization using the initial coordinates x and p. A compatibility condition similar to that related to the condition of incompressibility for the Navier- Stokes equations, is introduced. In that respect, a version of the projection method is considered to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. For the spatial discretization, a modified Godunov type method that exploits the discrete finite-volume derivatives by using the so-called Taylor Series Expansion Scheme (TSES), is then designed to solve the equations. We report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated.

Wydawca

Rocznik

Tom

1

Numer

1

Opis fizyczny

Daty

otrzymano
2015-07-23
zaakceptowano
2015-11-30
online
2015-12-31

Twórcy

  • Department of Mathematics, Pennsylvania State University, PA, USA
  • Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA, USA
  • Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, IL, USA
  • Temam: Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, Indiana, USA
  • Climate Dynamics and Predictability (CDP) section in the Division of Climate and Global Dynamics (CGD) at the National Center for Atmospheric Research (NCAR)

Bibliografia

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  • [6] Q. S. Chen, J. Laminie, A. Rousseau, R. Temam, and J. Tribbia. A 2.5D model for the equations of the ocean and the atmosphere. Anal. Appl. (Singap.), 5(3):199–229, 2007. [Crossref]
  • [7] Qingshan Chen, Ming-Cheng Shiue, and Roger Temam. The barotropic mode for the primitive equations. J. Sci. Comput., 45(1-3):167–199, 2010. [Crossref]
  • [8] Qingshan Chen, Ming-Cheng Shiue, Roger Temam, and Joseph Tribbia. Numerical approximation of the inviscid 3D primitive equations in a limited domain. ESAIM Math. Model. Numer. Anal., 46(3):619–646, 2012. [Crossref]
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  • [11] Michele Coti Zelati, Michel Frémond, Roger Temam, and Joseph Tribbia. The equations of the atmosphere with humidity and saturation: uniqueness and physical bounds. Phys. D, 264:49–65, 2013.
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Bibliografia

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bwmeta1.element.doi-10_1515_mcwf-2015-0005
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