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We present a collection of semi-Lagrangian methods for use with atmosphere models running at scale on new, heterogenous computing architectures. Each method prioritizes computational performance and efficiency by (a) employing spatially local numerical methods and (b) using large time steps relative to the advective CFL constraint. A newly developed cell-integrated scheme 1 for passive tracer advection on the sphere is presented and compared to the classical, interpolation-based semi-Lagrangian scheme. Each method confronts the problem of property preservation (e.g., mass conservation, monotonicity, tracer-air-mass consistency), which may be globally coupled, particularly if large time steps are used. We introduce a family of Constrained Density Reconstruction algorithms 2 that assure property preservation in both (a) as few batch reductions as possible and (b) independently of the data. Results from several standard tracer transport test cases are presented. The schemes serve as algorithmic prototypes, and we introduce plans for their development into a full 3D non-hydrostatic dynamical core.We present a collection of semi-Lagrangian methods for use with atmosphere models running at scale on new, heterogenous computing architectures. 

1 P. A. Bosler, A. M. Bradley, M. A. Taylor, Conservative multi-moment transport along characteristics for discontinuous Galerkin methods, submitted to SIAM J. Sci. Comput., 2018.
2 A. M. Bradley, P. A. Bosler, O. Guba, M. A. Taylor, G. A. Barnett, Communication-efficient property preservation in tracer transport, submitted to SIAM J. Sci. Comput., 2018.

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