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Title: An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables

Journal Article · · Journal of Advances in Modeling Earth Systems
 [1];  [1];  [1];  [2];  [3];  [4]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Univ. of California, Davis, CA (United States)
  3. NVIDIA, Santa Clara, CA (United States)
  4. Univ. Grenoble Alpes (France)

We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. The formulation is a version of Dubos and Tort (2014, https://doi.org/10.1175/MWR-D-14-00069.1) rewritten in terms of primitive variables. It is valid for terrain following mass or height coordinates and for both Eulerian or vertically Lagrangian discretizations. The discretization relies on an extension to Simmons and Burridge (1981, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2) vertical differencing, which we show obeys a discrete derivative product rule. This product rule allows us to simplify the treatment of the vertical transport terms. Energy conservation is obtained via a term-by-term balance in the kinetic, internal, and potential energy budgets, ensuring an energy-consistent discretization up to time truncation error with no spurious sources of energy. We demonstrate convergence with respect to time truncation error in a spectral element code with a horizontal explicit vertically implicit implicit-explicit time stepping algorithm.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Biological and Environmental Research (BER); USDOE National Nuclear Security Administration (NNSA); French National Research Agency
Grant/Contract Number:
AC04-94AL85000; NA0003525; ANR-14-CE23-0010
OSTI ID:
1631000
Report Number(s):
SAND2020-5242J; 686193
Journal Information:
Journal of Advances in Modeling Earth Systems, Vol. 12, Issue 1; ISSN 1942-2466
Publisher:
American Geophysical Union (AGU)Copyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (5)