A Cell-Integrated Semi-Lagrangian Semi-Implicit Fluid-Flow Solver with Consistent and Conservative Transport

May Wong
Department of Earth, Ocean, and Atmospheric Sciences
University of British Columbia 
Vancouver, BC, Canada 

Semi-Lagrangian semi-implicit (SLSI) models are popular for both global and regional numerical weather prediction applications primarily due to their stability and computational efficiency with larger time steps. While traditional SLSI schemes are not inherently mass-conserving due to their use of grid-point interpolation, several recently developed cell-integrated semi-Lagrangian (CISL) transport schemes evaluate the mass continuity equation in an inherently mass-conserving manner. However, semi-implicit fluid-flow solvers using these CISL schemes have relied on an implicit correction in the continuity equation that is based on the linearization around a time-independent mean reference state. This dependence makes mass conservation more difficult and forgoes numerical consistency between mass and constituent mass transport, leading to possible spurious generation or removal of constituent mass.

A new semi-implicit CISL solver proposed here uses the Conservative Semi-Lagrangian Multi-tracer scheme (CSLAM; a CISL approach) as the transport scheme and uses it to evaluate a flux-form implicit correction in the continuity equation. The algorithm is constructed to be similar to typical conservative SLSI schemes, requiring at each time step a single linear Helmholtz equation solution and a single application of CSLAM. The new scheme has been tested in a 2D shallow-water model (CSLAM-SW) and results from consistency tests using several idealized highly-nonlinear test flow problems showed that the specific concentration of an initially constant constituent field is preserved up to machine round off, whereas a solver using a typical CISL continuity equation formulation can have errors many orders of magnitude larger. Shape-preserving schemes are also applied in CSLAM-SW to ensure shape-preservation. The new semi-implicit CISL solver is currently being tested on the fully-compressible, nonhydrostatic equations and specifically for the desirable properties of mass conservation, consistency, and shape-preservation of moisture variables and tracers. The formulation and results from several idealized test cases using the nonhydrostatic solver will be presented.

Thursday, 14 February 2013, 3:30 PM
Refreshments 3:15 PM
NCAR-Foothills Laboratory, 3450 Mitchell Lane, Bldg 2 Auditorium, Room 1022

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Presenter(s): 
May Wong

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1022

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Thursday, February 14, 2013 - 3:30pm