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

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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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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Keywords

  • Inviscid hydrostatic primitive equations
  • Terrain following coordinates
  • Finite volume methods
  • Bottom topography