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Numerical Simulations of the Two-Dimensional Inviscid Hydrostatic Primitive Equations with Humidity and Saturation

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Abstract

The two-dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation are considered in the presence of topography. The model studied here describes the dynamics of the air or water in order to approximate global atmospheric flows. The heart of the paper is to derive a new set of transformed inviscid primitive equations using a version of the terrain-following coordinate systems and to develop an accurate numerical scheme to the equations. In this regard, a fully discrete numerical algorithm based on a Godunov-type finite volume method is proposed and its convergence tested. We then use this algorithm to simulate the flows above a mountain using the terrain-following coordinate system with a dynamic bottom pressure.

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Acknowledgements

Y.H. gratefully acknowledges support from the Research Fund of San Diego State University. R.M.T. gratefully acknowledges support from the National Science Foundation through grant No. DMS-1510249 and from the Research Fund of Indiana University.

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Authors and Affiliations

  1. Department of Mathematics, Lake Forest College, Lake Forest, USA

    Arthur Bousquet

  2. Department Mathematics and Statistics, San Diego State University, San Diego, USA

    Youngjoon Hong

  3. Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, USA

    Roger Temam

  4. Climate and Global Dynamics Division, National Center for Atmospheric Research, Boulder, USA

    Joseph Tribbia

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  1. Arthur Bousquet
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  2. Youngjoon Hong
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  3. Roger Temam
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  4. Joseph Tribbia
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Correspondence to Youngjoon Hong.

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Bousquet, A., Hong, Y., Temam, R. et al. Numerical Simulations of the Two-Dimensional Inviscid Hydrostatic Primitive Equations with Humidity and Saturation. J Sci Comput 83, 36 (2020). https://doi.org/10.1007/s10915-020-01215-y

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  • DOI: https://doi.org/10.1007/s10915-020-01215-y

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