Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that cannot rely on exact quadrature, due to the curved mesh. Using the strong form of the discontinuous Galerkin discretization, we achieve a splitting of the well-balanced condition into individual problems for the flux and volume terms, which has significant advantages: It allows for the construction of non-conforming, well-balanced flux discretizations, i.e. we can perform non- conforming mesh refinement while preserving the well-balanced property of the scheme. More importantly, this approach enables the development of a new method for handling wet/dry transitions. In contrast to other wetting/drying methods, it is well-balanced and able to handle wetting/drying robustly at any polynomial order, without the introduction of physical model assumptions such as viscosity, artificial porosity or cancellation of gravity. We perform a series of one-dimensional tests and analyze the properties of our scheme. In order to validate our method for the simulation of large-scale tsunami events on the rotating sphere, we perform numerical simulations of the 2011 Tohoku tsunami and compare our results to real-world buoy data. The method is able to predict arrival times and wave amplitudes accurately even over long distances. This indicates that our method accurately captures all physical phenomena relevant to the long-term evolution of tsunami waves

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

Numerical weather prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it will be necessary to use a single model for both applications. The new dynamical cores at the heart of these unified models are designed to scale efficiently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite differences, spectral transform, finite volumes and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods.Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to choose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (Meteorol Atmos Phys 82:287–301, 2003), this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.The authors would like to thank Prof. Eugenio Oñate (U. Politècnica de Catalunya) for his invitation to submit this review article. They are also thankful to Prof. Dale Durran (U. Washington), Dr. Tommaso Benacchio (Met Office), and Dr. Matias Avila (BSC-CNS) for their comments and corrections, as well as insightful discussion with Sam Watson, Consulting Software Engineer (Exa Corp.) Most of the contribution to this article by the first author stems from his Ph.D. thesis carried out at the Barcelona Supercomputing Center (BSCCNS) and Universitat Politècnica de Catalunya, Spain, supported by a BSC-CNS student grant, by Iberdrola Energías Renovables, and by grant N62909-09-1-4083 of the Office of Naval Research Global. At NPS, SM, AM, MK, and FXG were supported by the Office of Naval Research through program element PE-0602435N, the Air Force Office of Scientific Research through the Computational Mathematics program, and the National Science Foundation (Division of Mathematical Sciences) through program element 121670. The scalability studies of the atmospheric model NUMA that are presented in this paper used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. SM, MK, and AM are grateful to the National Research Council of the National Academies.Peer ReviewedPostprint (author's final draft

دیدگاه کارورزان، دستیاران و اعضای هیأت علمی بخش زنان در خصوص عوامل مؤثر بر شکل‌گیری اخلاق حرفه‌ای در بالین

مقدمه: آموزش اخلاق حرفه­ای بخش مهمی از برنامه­های فراگیران پزشکی است و حرفه ای‌گری (پروفیشنالیسم) از شایستگی­های محوری دوره پزشکی محسوب می­شود. شناسایی عوامل مؤثر بر فراگیری حرفه ای‌گری در بخش زنان و زایمان که از چالش­های اخلاقی خاص خود برخوردار است، می­تواند به کارآمدی برنامه­های آموزشی کمک کند. مطالعه حاضر با هدف تبیین دیدگاه و تجربیات اساتید و فراگیران پزشکی در بخش زنان و زایمان در خصوص عوامل مؤثر بر شکل‌گیری اخلاق حرفه­ای در بالین انجام شد. روش‌کار: در این مطالعه کیفی (1392)، 10 نفر از اساتید زنان و زایمان و 30 نفر از دستیاران تخصصی و کارورزان بخش زنان و زایمان مرکز آموزشی درمانی شهید صیاد شیرازی مشارکت نمودند. برای جمع‌آوری داده‌ها از روش مصاحبه­های انفرادی نیمه‌ساختار تا رسیدن به اشباع داده­ها استفاده شد. مصاحبه­ها خط به خط، دست‌نویس و مطابق رویکرد "تحلیل محتوای مرسوم" کدگذاری و طبقه‌بندی شدند. یافته‌ها: از تحلیل داده­ها چهار مضمون اصلی"ماهیت انسانی کار، شخصیت و منش فردی، داشتن الگو و مدل و عوامل آموزشی اجتماعی" استخراج شد که تبیین کننده عوامل مؤثر بر شکل‌گیری اخلاق حرفه­ای در بخش زنان و زایمان از دیدگاه اساتید و دانشجویان و دستیاران پزشکی بود. نتیجه‌گیری: الگو بودن اساتید و برنامه­های آموزشی بالینی در بخش زنان و زایمان، از مهم‌ترین عوامل مؤثر بر شکل‌گیری اخلاق حرفه­ای است، لذا به نظر می­رسد با مداخلات آموزشی مناسب روی این دو مؤلفه مهم بتوان به ارتقاء آموزش اخلاق حرفه­ای در بالین کمک کرد. کلیدواژه ها آموزش اخلاق؛ اخلاق حرفه‌ای؛ برنامه­های دستیاری؛ حرفه‌ ای گری؛ زنان و زایمان؛ کارورز پزشکی عنوان مقاله [English

Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application in to Atmospheric Simulations

Non-hydrostatic Unified Model of the Atmosphere (NUMA)The first NUMA papers appeared in 2008. From 2008 through 2010, all the NUMA papers appearing involved the 2D (x-z slice) Euler equations. All the theory and numerical implementations were first developed in 2D.The resolutions of interests in atmospheric simulations require prohibitively large computational resources. Adaptive mesh refinement (AMR) tries to mitigate this problem by putting high resolution in crucial areas of the domain. We investigate the performance of a tree-based AMR algorithm for the high order discontinuous Galerkin method on quadrilateral grids with non-conforming elements. We perform a detailed analysis of the cost of AMR by comparing this to uniform reference simulations of two standard atmospheric test cases: density current and rising thermal bubble. The analysis shows up to 15 times speed-up of the AMR simulations with the cost of mesh adaptation below 1% of the total runtime. We pay particular attention to the implicit-explicit (IMEX) time integration methods and show that the ARK2 method is more robust with respect to dynamically adapting meshes than BDF2. Preliminary analysis of preconditioning reveals that it can be an important factor in the AMR overhead. The compiler optimizations provide significant runtime reduction and positively affect the effectiveness of AMR allowing for speed-ups greater than it would follow from the simple performance model

Mass Conservation of the Unified Continuous and Discontinuous Element-Based Galerkin Methods on Dynamically Adaptive Grids with Application to Atmospheric Simulations

The article of record as published may be located at http://dx.doi.org/10.1016/j.jcp.2015.05.010We perform a comparison of mass conservation properties of the continuous (CG) and discontinuous (DG) Galerkin methods on non-conforming, dynamically adaptive meshes for two atmospheric test cases. The two methods are implemented in a unified way which allows for a direct comparison of the non-conforming edge treatment. We outline the implementation details of the non-conforming direct stiffness summation algorithm for the CG method and show that the mass conservation error is similar to the DG method. Both methods conserve to machine precision, regardless of the presence of the non-conforming edges. For lower order polynomials the CG method requires additional stabilization to run for very long simulation times. We addressed this issue by using filters and/or additional artificial viscosity. The mathematical proof of mass conservation for CG with non-conforming meshes is presented in Appendix B

Ice-Sheet / Ocean Interaction Model for Greenland Fjords Using High-Order Discontinuous Galerkin Methods

What are the major goals of the project? The overarching science goal of the project is to advance Earth System science by proposing a more realistic representation of physical processes in a Greenland fjord to enable future studies of ice-sheet/ocean interactions and their impact on the Greenland Ice Sheets (GrIS) (in many fjords) and on pan-Arctic climate variability. To achieve this objective, we proposed to build a new, separate, high-resolution ocean model for use in Earth System Models (ESMs) to realistically represent the complex three-dimensional physics of the fjord, its bathymetry, coastlines, and coupling with both ice-shelf and the outer ocean around Greenland using discontinuous Galerkin (DG) methods

Evaluation of the utility of static and adaptive mesh refinement for idealized tropical cyclone problems in a spectral element shallow water model

The utility of static and adaptive mesh refinement (SMR and AMR, respectively) are examined for idealized tropical cyclone (TC) simulations in a spectral element f-plane shallow water model. The SMR simulations have varying sizes of the statically refined meshes (geometry-based) while the AMR simulations use a potential vorticity (PV) threshold to adaptively refine the mesh to the evolving TC. Numerical simulations are conducted for four cases: (i) TC-like vortex advecting in a uniform flow, (ii) binary vortex interaction, (iii) barotropic instability of a PV ring, and (iv) barotropic instability of a thin strip of PV. For each case, a high resolution “truth” simulation is compared to two different SMR simulations and three different AMR simulations for accuracy and efficiency. The multiple SMR and AMR simulations have variations in the number of fully-refined elements in the vicinity of the TC. For these idealized cases, it is found that the SMR and AMR simulations are able to resolve the vortex dynamics as well as the “truth” runs, with no significant loss in accuracy in the refined region in the vortex vicinity and with significant speed-ups (factor of 2-5). The overall accuracy is enhanced by a greater area of fully refined mesh in both the SMR and AMR simulations. While these results are highly idealized, they demonstrate the potential for SMR and AMR for the numerical simulation of TCs in three dimensions and more complex models

Strong scaling for numerical weather prediction at petascale with the atmospheric model NUMA

Numerical weather prediction (NWP) has proven to be computationally challenging due to its inherent multiscale nature. Currently, the highest resolution NWP models use a horizontal resolution of approximately 15 km. At the resolution many important processes in the atmosphere are not resolved. Needless to say this introduces errors. In order to increase the resolution of NWP models highly scalable atmospheric models are needed. The Non-hydrostatic Unified Model of the Atmosphere (NUMA), developed by the authors at the Naval Postgraduate School, was designed to achieve this purpose. NUMA is used by the Naval Research Laboratory, Monterey, as the engine inside its next generation weather prediction system NEPTUNE. NUMA solves the fully compressible Navier-Stokes equations be means of high-order Galerkin methods (both spectral element as well as discontinuous Galerkin methods can be used. Mesh generation is done using the p4est library. NUMA is capable of running middle and upper atmosphere simulations since it does not make use of the shallow-atmosphere approximation. This paper presents the performance analysis and optimization of the spectral element version of NUMA. The performance at different optimization stages is analyzed using hardware counters with the help of the Hardware Performance Monitor Toolkit as well as the PAPI library. Machine independent optimization is compared to machine specific optimization using BG/Q vector intrinsics. By using vector intrinsics the main computations reach 1.2 PFlops on the entire machine Mira. The paper also present scalability studies for two idealized test cases that are relevant for NWP applications. The atmospheric model NUMA delivers an excellent strong scaling efficiency of 99% on the entire supercomputer Mira using a mesh with 1.8 billion grid points. This allows us to run a global forecast of a baroclinic wave test case at 3 km uniform horizontal resolution and double precision within the time frame required for operational weather prediction.Financial support for the work presented in this paper was provided by the Office of Naval Research through Program Element PE-0602435N, The Air Force Office of Scientific Research through the Computation Mathematics program, and the National Science Foundation (Division of MAthematical Sciences) through program elelment 121760. AM, MK and SM are grateful to the National Research Council of the National Academies.Approved for public release; distribution is unlimited

A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations

None foundThe high-order numerical solution of the non-linear shallow water equations is susceptible to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by presenting a shock capturing model based on the numerical residual of the solution. Via numerical tests, we demonstrate that the model removes the spurious oscillations in the proximity of strong wave fronts while preserving their strength. Furthermore, for coarse grids, it prevents energy from building up at small wave-numbers. The model has no tunable parameter and, if applied to the continuity equation to stabilize the water surface, the addition of the shock capturing scheme does not affect mass conservation. We found that our model improves the continuous and discontinuous Galerkin solutions alike in the proximity of sharp fronts propagating on wet surfaces. In the presence of wet/dry interfaces, however, the model needs to be enhanced with the addition of an inundation scheme. In this paper, we simply rely on the presence of a relatively small layer of water in the regions that should be dry.Office of Naval ResearchAir Force Office of Scientific Researc