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2015 | 1 | 1 |

Article title

Numerical simulations of the humid
atmosphere above a mountain


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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.







Physical description


23 - 7 - 2015
30 - 11 - 2015
31 - 12 - 2015


  • 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)


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