The authors are thankful for Dr. Richard Loft (NCAR) for the SIParCS internship support for Wei Guo. R. Nair is partially supported by the DOE BER Program DE-SC0001658. W. Guo and J.-M. Qiu are partially supported by Air Force Office of Scientific Computing YIP Grant FA9550-12-0318, NSF Grant DMS-0914852, and DMS-1217008, University of Houston.
Blossey, P., , and D. Durran, 2008: Selective monotonicity preservation in scalar advection. J. Comput. Phys., 227 (10), 5160–5183.
Childs, P., , and K. Morton, 1990: Characteristic Galerkin methods for scalar conservation laws in one dimension. SIAM J. Numer. Anal., 27 (3), 553–594.
Cockburn, B., , and C.-W. Shu, 2001: Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput., 16 (3), 173–261.
Dennis, J., and Coauthors, 2011: CAM-SE: A scalable spectral-element dynamical core for the Community Atmosphere Model. Int. J. High Perform. Comput. Appl., 26, 74–89.
Erath, C., , and R. D. Nair, 2014: A conservative multi-tracer transport scheme for spectral-element spherical grids. J. Comput. Phys., 256, 118–134, doi:10.1016/j.jcp.2013.08.050.
Giraldo, F., , and M. Restelli, 2008: A study of spectral element and discontinuous Galerkin method for the Navier–Stokes equations in nonhydrostatic mesoscale modeling: Equation sets and test cases. J. Comput. Phys., 227, 3847–3877.
Hall, D. M., , and R. D. Nair, 2013: Discontinuous Galerkin transport on the spherical Yin–Yang overset mesh. Mon. Wea. Rev., 141, 264–282.
Lauritzen, P., , R. Nair, , and P. Ullrich, 2010: A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid. J. Comput. Phys., 229 (5), 1401–1424.
Nair, R., , and C. Jablonowski, 2008: Moving vortices on the sphere: A test case for horizontal advection problems. Mon. Wea. Rev., 136, 699–711.
Nair, R., , and P. Lauritzen, 2010: A class of deformational flow test cases for linear transport problems on the sphere. J. Comput. Phys., 229 (23), 8868–8887.
Nair, R., , S. Thomas, , and R. Loft, 2005: A discontinuous Galerkin transport scheme on the cubed sphere. Mon. Wea. Rev., 133, 814–828.
Nair, R., , H.-W. Choi, , and H. M. Tufo, 2009: Computational aspects of a scalable high-order discontinuous Galerkin atmospheric dynamical core. Comput. Fluids, 38, 309–319.
Pudykiewicz, J., 2011: On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid. J. Comput. Phys., 230 (5), 1956–1991.
Qiu, J., , and C. Shu, 2011: Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system. J. Comput. Phys., 230 (23), 8386–8409.
Restelli, M., , L. Bonaventura, , and R. Sacco, 2006: A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows. J. Comput. Phys., 216, 195–215.
Ronchi, C., , R. Iacono, , and P. Paolucci, 1996: The cubed sphere: A new method for the solution of partial differential equations in spherical geometry. J. Comput. Phys., 124, 93–114.
Rossmanith, J., , and D. Seal, 2011: A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov–Poisson equations. J. Comput. Phys., 230, 6203–6232.
Russell, T., , and M. Celia, 2002: An overview of research on Eulerian–Lagrangian localized adjoint methods (ELLAM). Adv. Water Resour., 25 (8), 1215–1231.
Sadourny, R., 1972: Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev., 100, 136–144.
Tumolo, G., , L. Bonaventura, , and M. Restelli, 2013: A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallow water equations. J. Comput. Phys., 232, 46–67.
Williamson, D., , J. Drake, , J. Hack, , R. Jakob, , and P. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys., 102, 211–224.
Zhang, X., , and C.-W. Shu, 2010a: On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys., 229, 3091–3120.
Zhang, X., , and C.-W. Shu, 2010b: On positivity preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. J. Comput. Phys., 229, 8918–8934.
Zhang, Y., , and R. D. Nair, 2012: A nonoscillatory discontinuous Galerkin transport scheme on the cubed sphere. Mon. Wea. Rev., 140, 3106–3126.