Isotropic spherical grids considered for next generation weather and climate models challenge the advection operator in new ways compared to the traditional regular latitude-longitude grids. These newer grids are primarily non-orthogonal which might question the accuracy of dimensionally split schemes implemented on such grids. Also, zonally symmetric flows, that on a lat-lon grid are always parallel or orthogonal to grid lines, are at best locally parallel to grid lines on the non-traditional grids. For balanced flows the lack of zonal alignment might spuriously perturb balances that lat-lon based models are able to maintain (Lauritzen et al. 2010a). To minimize the level of spurious `grid-imprinting’ and to resolve highly deformational flow structures, fully two-dimensional schemes may be an attractive choice.
In this talk a new conservative semi-Lagrangian multi-tracer scheme is introduced (Lauritzen et al. 2010b) which can be cast in either Lagrangian and flux-form (Lauritzen et al. 2010c, Harris and Lauritzen, 2010). Initially the scheme has been implemented on the cubed-sphere, however, it can be generalized to other unstructured grids reusing much of the same technology. The scheme is largely based on the computation of geometric quantities that can be reused for each additional tracer. In the context of testing the scheme a set of (or suite of) new deformational flow problems on the sphere has been developed (Nair and Lauritzen, 2010). These flow fields are divergent or non-divergent and, contrary to the popular solid-body advection test case, employ non-trivial trajectories.
Harris, L.M, and P.H. Lauritzen, 2010: A Flux-form version of the Conservative Semi-Lagrangian Multi-tracer transport scheme (CSLAM) on the cubed sphere grid. J. Comput. Phys, submitted.
Lauritzen, P.H., C. Jablonowski, M.A. Taylor and R.D. Nair, 2010a: Rotated versions of the Jablonowski steady-state and baroclinic wave test cases: A dynamical core intercomparison. Journal of Advances in Modeling Earth Systems: in press.
Lauritzen, P.H., R.D. Nair and P.A. Ullrich, 2010b: A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid. J. Comput. Phys.: Vol. 229, Issue 5, pp. 1401–1424, DOI: 10.1016/j.jcp.2009.10.036.
Lauritzen, P.H., P.A. Ullrich and R.D. Nair, 2010c: Atmospheric transport schemes: Desirable properties and a semi-Lagrangian view on finite-volume discretizations. Chapter in Springer book Numerical Techniques for Global Atmospheric Models: submitted.
Nair, R.D. and P.H. Lauritzen, 2010: A Class of Deformational Flow Test-Cases for the Advection Problems on the Sphere. J. Comput. Phys.: submitted.