Communications of the ACM
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Towards an Efficient and Scalable Discontinuous Galerkin Atmospheric Model
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
International Journal of High Performance Computing Applications
Journal of Computational Physics
High-order Galerkin methods for scalable global atmospheric models
Computers & Geosciences
A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
Journal of Computational Physics
A time-split nonhydrostatic atmospheric model for weather research and forecasting applications
Journal of Computational Physics
Validity of the single processor approach to achieving large scale computing capabilities
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
Journal of Computational Physics
A Fully Implicit Jacobian-Free High-Order Discontinuous Galerkin Mesoscale Flow Solver
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
A Scalable and Adaptable Solution Framework within Components of the Community Climate System Model
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
A large time step 1D upwind explicit scheme (CFL1): Application to shallow water equations
Journal of Computational Physics
Journal of Computational Physics
A conservative multi-tracer transport scheme for spectral-element spherical grids
Journal of Computational Physics
Journal of Computational Physics
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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 CFL2. 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.