206 research outputs found
Partial Observability and its Consistency for PDEs
In this paper, a quantitative measure of partial observability is defined for
PDEs. The quantity is proved to be consistent if the PDE is approximated using
well-posed approximation schemes. A first order approximation of an
unobservability index using an empirical Gramian is introduced. Several
examples are presented to illustrate the concept of partial observability,
including Burgers' equation and a one-dimensional nonlinear shallow water
equation.Comment: 5 figures, 25 pages. arXiv admin note: substantial text overlap with
arXiv:1111.584
Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
We present semi-implicit (implicit-explicit) formulations of the compressible Navier-Stokes equations (NSE) for applications in nonhydrostatic atmospheric modeling. The compressible NSE in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling
if one wishes to extract the Schur complement form of the linear implicit problem. We present results for five different forms of the compressible NSE and describe in detail how to formulate the semi-implicit time-integration method for these equations. Finally, we compare all five equations and
compare the semi-implicit formulations of these equations both using the Schur and No Schur forms against an explicit Runge-Kutta method. Our simulations show that, if efficiency is the main criterion, it matters which form of the governing equations you choose. Furthermore, the semi-implicit
formulations are faster than the explicit Runge-Kutta method for all the tests studied, especially if the Schur form is used. While we have used the spectral element method for discretizing the spatial operators, the semi-implicit formulations that we derive are directly applicable to all other numerical methods. We show results for our five semi-implicit models for a variety of problems of interest in nonhydrostatic atmospheric modeling, including inertia-gravity waves, density current (i.e., Kelvin-Helmholtz instabilities), and mountain test cases; the latter test case requires the implementation of nonreflecting boundary conditions. Therefore, we show results for all five semi-implicit models using the appropriate boundary conditions required in nonhydrostatic atmospheric modeling: no-flux
(reflecting) and nonreflecting boundary conditions (NRBCs). It is shown that the NRBCs exert a strong impact on the accuracy and efficiency of the models.Office of Naval ResearchJunta de AndalucÃaGerman Research Foundatio
The Impacts of Dry Dynamic Cores on Asymmetric Hurricane Intensification
The article of record as published may be found at http://dx.doi.org/10.1175/JAS-D-16-0055.1The fundamental pathways for tropical cyclone (TC) intensification are explored by considering axisym- metric and asymmetric impulsive thermal perturbations to balanced, TC-like vortices using the dynamic cores of three different nonlinear numerical models. Attempts at reproducing the results of previous work, which used the community WRF Model, revealed a discrepancy with the impacts of purely asymmetric thermal forcing. The current study finds that thermal asymmetries can have an important, largely positive role on the vortex intensification, whereas other studies find that asymmetric impacts are negligible.
Analysis of the spectral energetics of each numerical model indicates that the vortex response to asym- metric thermal perturbations is significantly damped in WRF relative to the other models. Spectral kinetic energy budgets show that this anomalous damping is primarily due to the increased removal of kinetic energy from the vertical divergence of the vertical pressure flux, which is related to the flux of inertia–gravity wave energy. The increased kinetic energy in the other two models is shown to originate around the scales of the heating and propagate upscale with time from nonlinear effects. For very large thermal amplitudes (50 K), the anomalous removal of kinetic energy due to inertia–gravity wave activity is much smaller, resulting in good agreement between models.
The results of this paper indicate that the numerical treatment of small-scale processes that project strongly onto inertia–gravity wave energy can lead to significant differences in asymmetric TC intensification. Sensitivity tests with different time integration schemes suggest that diffusion entering into the implicit solution procedure is partly responsible for the anomalous damping of energy.Institute of Geophysics, Planetary Physics and Signatures (IGPPS) at Los Alamos National LaboratoryOffice of Naval Research through program element PE-0602435Institute of Geophysics, Planetary Physics and Signatures (IGPPS) at Los Alamos National LaboratoryOffice of Naval Research through program element PE-060243
IMplicit-EXplicit Formulations for Discontinuous Galerkin Non-Hydrostatic Atmospheric Models
This work presents IMplicit-EXplicit (IMEX) formulations for discontinuous
Galerkin (DG) discretizations of the compressible Euler equations governing
non-hydrostatic atmospheric flows. In particular, we show two different IMEX
formulations that not only treat the stiffness due to the governing dynamics
but also the domain discretization. We present these formulations for two
different equation sets typically employed in atmospheric modeling. For both
equation sets, efficient Schur complements are derived and the challenges and
remedies for deriving them are discussed. The performance of these IMEX
formulations of different orders are investigated on both 2D (box) and 3D
(sphere) test problems and shown to achieve their theoretical rates of
convergence and their efficiency with respect to both mesoscale and global
applications are presented
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