@article{norman_nair_semazzi_2011, title={A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics}, volume={230}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2010.11.022}, abstractNote={An explicit finite-volume solver is proposed for numerical simulation of non-hydrostatic atmospheric dynamics with promise for efficiency on massively parallel machines via low communication needs and large time steps. Solving the governing equations with a single stage lowers communication, and using the method of characteristics to follow information as it propagates enables large time steps. Using a non-oscillatory interpolant, the method is stable without post-hoc filtering. Characteristic variables (built from interface flux vectors) are integrated upstream from interfaces along their trajectories to compute time-averaged fluxes over a time step. Thus we call this method a Flux-Based Characteristic Semi-Lagrangian (FBCSL) method. Multidimensionality is achieved via a second-order accurate Strang operator splitting. Spatial accuracy is achieved via the third- to fifth-order accurate Weighted Essentially Non-Oscillatory (WENO) interpolant. We implement the theory to form a 2-D non-hydrostatic compressible (Euler system) atmospheric model in which standard test cases confirm accuracy and stability. We maintain stability with time steps larger than CFL = 1 (CFL number determined by the acoustic wave speed, not advection) but note that accuracy degrades unacceptably for most cases with CFL > 2. For the smoothest test case, we ran out to CFL = 7 to investigate the error associated with simulation at large CFL number time steps. Analysis suggests improvement of trajectory computations will improve error for large CFL numbers.}, number={4}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Norman, Matthew R. and Nair, Ramachandran D. and Semazzi, Fredrick H. M.}, year={2011}, month={Feb}, pages={1567–1584} }
 @article{norman_semazzi_nair_2009, title={Conservative cascade interpolation on the sphere: An intercomparison of various non-oscillatory reconstructions}, volume={135}, ISSN={["1477-870X"]}, DOI={10.1002/qj.402}, abstractNote={Abstract}, number={640}, journal={QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY}, author={Norman, Matthew R. and Semazzi, Fredrick H. M. and Nair, Ramachandran D.}, year={2009}, month={Apr}, pages={795–805} }
 @article{norman_nair_2008, title={Inherently Conservative Nonpolynomial-Based Remapping Schemes: Application to Semi-Lagrangian Transport}, volume={136}, ISSN={["1520-0493"]}, DOI={10.1175/2008MWR2499.1}, abstractNote={Abstract}, number={12}, journal={MONTHLY WEATHER REVIEW}, author={Norman, Matthew R. and Nair, Ramachandran D.}, year={2008}, month={Dec}, pages={5044–5061} }
 @article{semazzi_scroggs_pouliot_mckee-burrows_norman_poojary_tsai_2005, title={On the accuracy of semi-Lagrangian numerical simulation of internal gravity wave motion in the atmosphere}, volume={83}, ISSN={["2186-9057"]}, DOI={10.2151/jmsj.83.851}, abstractNote={We have investigated the accuracy ofthe semi-implicit semi-Lagrangian (SISL) method in simulating internal gravity wave (IGW) motion. We have focused on the relative accuracy of the hydrostatic, and nonhydrostatic IGW solutions. The analysis is based on a linearized model and a Global Circulation Model-Dynamic Core (GCM-DC) with a stretched grid.The nonhydrostatic version of the GCM-DC model produces the familiar IGW train disturbance anchored to an isolated hypothetical mountain. The wave has a distinct tilt away from the vertical direction, which is consistent with classical theory. For the hydrostatic version of the model, the axis of the resulting IGW train rests nearly perpendicular to the mountain top, thus again consistent with classical theory. Increasing the time step from 10 s; Courant number (Cn) = 0.5; to 60 s (Cn = 3.0), results in stable solutions for both the hydrostatic and nonhydrostatic versions of the model. The nonhydrostatic solution is in close agreement with the control run however, the hydrostatic solution exhibits large phase truncation errors.The solutions for the one-dimensional linearized SISL model confirm the GCM-DC results that the nonhydrostatic IGW train is less damped and shifted by the SISL scheme than the corresponding hydrostatic IGW motion. The linear solutions indicate very high accuracy of the physical mode of the solution, but it rapidly deteriorates when Cn exceeds unity. As Δt → 0 the amplitude of the computational mode tends to zero and its frequency to infinity. However, as Δt → ∞, the frequency of the computational SISL mode asymptotically approaches the value of the frequency of the corresponding SISL physical mode. Furthermore, the amplitude of the SISL computational mode is directly proportional to the size of the time step. Therefore, at large time steps, the amplification of the computational mode could offset some of the numerical damping of the physical mode by the SISL scheme.}, number={5}, journal={JOURNAL OF THE METEOROLOGICAL SOCIETY OF JAPAN}, author={Semazzi, FHM and Scroggs, JS and Pouliot, GA and McKee-Burrows, AL and Norman, M and Poojary, V and Tsai, YM}, year={2005}, month={Oct}, pages={851–869} }