A cell-integrated semi-Lagrangian semi-implicit shallow-water model (CSLAM-SW) with conservative and consistent transport

A Cartesian semi-implicit solver using the Conservative Semi-Lagrangian Multitracer (CSLAM) transport scheme is constructed and tested for shallow-water (SW) flows. The SW equations solver (CSLAM-SW) uses a discrete semi-implicit continuity equation specifically designed to ensure a conservative and consistent transport of constituents by avoiding the use of a constant mean reference state. The algorithm is constructed to be similar to typical conservative semi-Lagrangian semi-implicit schemes, requiring at each time step a single linear Helmholtz equation solution and a single application of CSLAM. The accuracy and stability of the solver is tested using four test cases for a radially propagating gravity wave and two barotropically unstable jets. In a consistency test using the new solver, the specific concentration constancy is preserved up to machine roundoff, whereas a typical formulation can have errors many orders of magnitude larger. In addition to mass conservation and consistency, CSLAM-SW also ensures shape preservation by combining the new scheme with existing shape-preserving filters. With promising SW test results, CSLAM-SW shows potential for extension to a nonhydrostatic, fully compressible system solver for numerical weather prediction and climate models.

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Author Wong, May
Skamarock, William
Lauritzen, Peter
Stull, Roland
Publisher UCAR/NCAR - Library
Publication Date 2013-07-01T00:00:00
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Topic Category geoscientificInformation
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Metadata Date 2023-08-18T19:04:22.608245
Metadata Record Identifier edu.ucar.opensky::articles:13054
Metadata Language eng; USA
Suggested Citation Wong, May, Skamarock, William, Lauritzen, Peter, Stull, Roland. (2013). A cell-integrated semi-Lagrangian semi-implicit shallow-water model (CSLAM-SW) with conservative and consistent transport. UCAR/NCAR - Library. http://n2t.net/ark:/85065/d71v5fvj. Accessed 15 February 2025.

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