Ahmad, N., and J. Lindeman, 2007: Euler solutions using flux-based wave decomposition. International Journal for Numerical Methods in Fluids, 54, 47−72, https://doi.org/10.1002/fld.1392.
Bacon, D. P., and Coauthors, 2000: A dynamically adapting weather and dispersion model: The operational multiscale environment model with grid adaptivity (OMEGA). Mon. Wea. Rev., 128, 2044−2076, https://doi.org/10.1175/1520-0493(2000)128<2044:ADAWAD>2.0.CO;2.
Behrens, J., 1996: An adaptive semi-lagrangian advection scheme and its parallelization. Mon. Wea. Rev., 124, 2386−2395, https://doi.org/10.1175/1520-0493(1996)124<2386:AASLAS>2.0.CO;2.
Berger, M., and I. Rigoutsos, 1991: An algorithm for point clustering and grid generation. IEEE Transactions on Systems, Man, and Cybernetics, 21, 1278−1286, https://doi.org/10.1109/21.120081.
Berger, M. J., and J. Oliger, 1984: Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys., 53, 484−512, https://doi.org/10.1016/0021-9991(84)90073-1.
Berger, M. J., and P. Colella, 1989: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys., 82, 64−84, https://doi.org/10.1016/0021-9991(89)90035-1.
Berger, M. J., and R. J. LeVeque, 1998: Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems. SIAM Journal on Numerical Analysis, 35, 2298−2316, https://doi.org/10.1137/S0036142997315974.
Blaise, S., and A. St-Cyr, 2012: A dynamic hp-adaptive discontinuous Galerkin method for shallow-water flows on the sphere with application to a global tsunami simulation. Mon. Wea. Rev., 140, 978−996, https://doi.org/10.1175/MWR-D-11-00038.1.
Blayo, E., and L. Debreu, 1999: Adaptive mesh refinement for finite-difference ocean models: First experiments. J. Phys. Oceanogr., 29, 1239−1250, https://doi.org/10.1175/1520-0485(1999)029<1239:AMRFFD>2.0.CO;2.
Carpenter, R. L. Jr., K. K. Droegemeier, P. R. Woodward, and C. E. Hane, 1990: Application of the piecewise parabolic method (PPM) to meteorological modeling. Mon. Wea. Rev., 118, 586−612, https://doi.org/10.1175/1520-0493(1990)118<0586:AOTPPM>2.0.CO;2.
Chen, C. G., and F. Xiao, 2008: Shallow water model on cubed-sphere by multi-moment finite volume method. J. Comput. Phys., 227, 5019−5044, https://doi.org/10.1016/j.jcp.2008.01.033.
Chen, C. G., F. Xiao, and X. L. Li, 2011: An adaptive multimoment global model on a cubed sphere. Mon. Wea. Rev., 139, 523−548, https://doi.org/10.1175/2010MWR3365.1.
Giraldo, F. X., and T. E. Rosmond, 2004: A scalable spectral element Eulerian atmospheric model (SEE-AM) for NWP: Dynamical core tests. Mon. Wea. Rev., 132, 133−153, https://doi.org/10.1175/1520-0493(2004)132<0133:ASSEEA>2.0.CO;2.
Giraldo, F. X., and M. Restelli, 2008: A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases. J. Comput. Phys., 227, 3849−3877, https://doi.org/10.1016/j.jcp.2007.12.009.
Hubbard, M. E., and N. Nikiforakis, 2003: A three-dimensional, adaptive, Godunov-type model for global atmospheric flows. Mon. Wea. Rev., 131, 1848−1864, https://doi.org/10.1175//2568.1.
Ii, S., and F. Xiao, 2007: CIP/multi-moment finite volume method for Euler equations: A semi-Lagrangian characteristic formulation. J. Comput. Phys., 222, 849−871, https://doi.org/10.1016/j.jcp.2006.08.015.
Ii, S., and F. Xiao, 2009: High order multi-moment constrained finite volume method. Part I: Basic formulation. J. Comput. Phys., 228, 3669−3707, https://doi.org/10.1016/j.jcp.2009.02.009.
Ii, S., M. Shimuta, and F. Xiao, 2005: A 4th-order and single-cell-based advection scheme on unstructured grids using multi-moments. Computer Physics Communications, 173, 17−33, https://doi.org/10.1016/j.cpc.2005.07.003.
Iskandarani, M., D. B. Haidvogel, J. C. Levin, E. Curchitser, and C. A. Edwards, 2002: Multi-scale geophysical modeling using the spectral element method. Computing in Science & Engineering, 4, 42−48, https://doi.org/10.1109/MCISE.2002.1032428.
Jablonowski, C., M. Herzog, J. E. Penner, R. C. Oehmke, Q. F. Stout, B. van Leer, and K. G. Powell, 2006: Block-structured adaptive grids on the sphere: Advection experiments. Mon. Wea. Rev., 134, 3691−3713, https://doi.org/10.1175/MWR3223.1.
Kessler, M., 1999: Development and analysis of an adaptive transport scheme. Atmos. Environ., 33, 2347−2360, https://doi.org/10.1016/S1352-2310(98)00415-4.
Levy, M. N., R. D. Nair, and H. M. Tufo, 2007: High-order Galerkin methods for scalable global atmospheric models. Computers & Geosciences, 33, 1022−1035, https://doi.org/10.1016/j.cageo.2006.12.004.
Li, X. L., C. G., Chen, X. S., Shen and F., Xiao, 2013: A Multimoment constrained finite-volume model for nonhydrostatic atmospheric dynamics. Mon. Wea. Rev, 141, 1216−1240, https://doi.org/10.1175/MWR-D-12-00144.1.
Nair, R. D., H. W. Choi, and H. M. Tufo, 2009: Computational aspects of a scalable high-order discontinuous Galerkin atmospheric dynamical core. Computers & Fluids, 38, 309−319, https://doi.org/10.1016/j.compfluid.2008.04.006.
Norman, M. R., R. D. Nair, and F. H. M. Semazzi, 2011: A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics. J. Comput. Phys., 230, 1567−1584, https://doi.org/10.1016/j.jcp.2010.11.022.
Pielke, R. A., and Coauthors, 1992: A comprehensive meteorological modeling system-RAMS. Meteorol. Atmos. Phys., 49, 69−91, https://doi.org/10.1007/BF01025401.
Qin, Q. C., X. S. Shen, C. G. Chen, F. Xiao, Y. J. Dai, and X. L. Li, 2019: A 3D nonhydrostatic compressible atmospheric dynamic core by multi-moment constrained finite volume method. Adv. Atmos. Sci., 36, 1129−1142, https://doi.org/10.1007/s00376-019-9002-4.
Schär, C., D. Leuenberger, O. Fuhrer, D. Lüthi, and C. Girard, 2002: A new terrain-following vertical coordinate formulation for atmospheric prediction models. Mon. Wea. Rev., 130, 2459−2480, https://doi.org/10.1175/1520-0493(2002)130<2459:ANTFVC>2.0.CO;2.
Shu, C. W., 1988: Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing, 9, 1073−1084, https://doi.org/10.1137/0909073.
Skamarock, W. C., and J. B. Klemp, 1993: Adaptive grid refinement for two-dimensional and three-dimensional nonhydrostatic atmospheric flow. Mon. Wea. Rev., 121, 788−804, https://doi.org/10.1175/1520-0493(1993)121<0788:AGRFTD>2.0.CO;2.
Skamarock, W. C., and J. B. Klemp, 1994: Efficiency and accuracy of the Klemp-Wilhelmson time-splitting technique. Mon. Wea. Rev., 122, 2623−2630, https://doi.org/10.1175/1520-0493(1994)122<2623:EAAOTK>2.0.CO;2.
Skamarock, W., J. Oliger, and R. L. Street, 1989: Adaptive grid refinement for numerical weather prediction. J. Comput. Phys., 80, 27−60, https://doi.org/10.1016/0021-9991(89)90089-2.
St-Cyr, A., C. Jablonowski, J. M. Dennis, H. M. Tufo, and S. J. Thomas, 2008: A comparison of two shallow-water models with nonconforming adaptive grids. Mon. Wea. Rev., 136, 1898−1922, https://doi.org/10.1175/2007MWR2108.1.
Stevens, D. E., and S. Bretherton, 1996: A forward-in-time advection scheme and adaptive multilevel flow solver for nearly incompressible atmospheric flow. J. Comput. Phys., 129, 284−295, https://doi.org/10.1006/jcph.1996.0250.
Straka, J. M., R. B. Wilhelmson, L. J. Wicker, J. R. Anderson, and K. K. Droegemeier, 1993: Numerical solutions of a non-linear density current: A benchmark solution and comparisons. International Journal for Numerical Methods in Fluids, 17, 1−22, https://doi.org/10.1002/fld.1650170103.
Thomas, S. J., and R. D. Loft, 2000: Parallel semi-implicit spectral element methods for atmospheric general circulation models. J. Comput. Phys., 15, 499−518, https://doi.org/10.1023/A:1011188832645.
Tomlin, A., M. Berzins, J. Ware, J. Smith, and M. J. Pilling, 1997: On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources. Atmos. Environ., 31, 2945−2959, https://doi.org/10.1016/S1352-2310(97)00120-9.
Wicker, L. J., and W. C. Skamarock, 1998: A time-splitting scheme for the elastic equations incorporating second-order Runge-Kutta time differencing. Mon. Wea. Rev., 126, 1992−1999, https://doi.org/10.1175/1520-0493(1998)126<1992:ATSSFT>2.0.CO;2.
Williamson, D. L., J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys., 102, 211−224, https://doi.org/10.1016/S0021-9991(05)80016-6.
Xiao, F., R. Akoh, and S. Ii, 2006: Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows. J. Comput. Phys., 213, 31−56, https://doi.org/10.1016/j.jcp.2005.08.002.
Yabe, T., and T. Aoki, 1991: A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver. Computer Physics Communications, 66, 219−232, https://doi.org/10.1016/0010-4655(91)90071-R.
Yabe, T., F. Xiao, and T. Utsumi, 2001: The constrained interpolation profile method for multiphase analysis. J. Comput. Phys., 169, 556−593, https://doi.org/10.1006/jcph.2000.6625.
Yessad, K., and P. Bénard, 1996: Introduction of a local mapping factor in the spectral part of the Météo-France global variable mesh numerical forecast model. Quart. J. Roy. Meteor. Soc., 122, 1701−1719, https://doi.org/10.1002/QJ.49712253511.