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        Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2D Aspects

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        Author
        Choi, Suk-Jin
        Giraldo, Francis X.
        Kim, Junghan
        Shin, Seoleun
        Date
        2014-04
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        Abstract
        The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2D) slice (X-Z) framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The numerical results demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core. The present core provides a practical framework for further development of three-dimensional (3D) non-hydrostatic compressible atmospheric models.
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        Submitted to Monthly Weather Review
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        http://hdl.handle.net/10945/45513
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          Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects 

          Giraldo, F.X.; Choi, S.-J.; Kim, J.; Shin, S. (Copernicus Publications, 2014);
          The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and ...
        • Thumbnail

          Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects 

          Giraldo, F.X.; Choi, S.-J.; Kim, J.; Shin, S. (Copernicus Publications, 2014-06-10);
          The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a ...
        • Thumbnail

          Development and evaluation of a hydrostatic dynamical core using the spectral element/discontinuous Galerkin methods 

          Giraldo, F.X.; Choi, S.-J. (Copernicus Publications, 2014-06-26);
          In this paper, we present a dynamical core for the atmospheric primitive hydrostatic equations using a unified formulation of spectral element (SE) and discontinuous Galerkin (DG) methods in the horizontal direction with ...
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