Advances in the Approximation Theory for Functional Reconstructions Using GMLS and Applications to Meshless Discretization of Differential Equations
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Journal of Computational Physics
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracer integral, and preservation of nonlinear correlation in a pair of tracers. We compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.
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The Next Generation Global Atmosphere Model LDRD project developed a suite of atmosphere models: a shallow water model, an x-z hydrostatic model, and a 3D hydrostatic model, by using Albany, a finite element code. Albany provides access to a large suite of leading-edge Sandia high-performance computing technologies enabled by Trilinos, Dakota, and Sierra. The next-generation capabilities most relevant to a global atmosphere model are performance portability and embedded uncertainty quantification (UQ). Performance portability is the capability for a single code base to run efficiently on diverse set of advanced computing architectures, such as multi-core threading or GPUs. Embedded UQ refers to simulation algorithms that have been modified to aid in the quantifying of uncertainties. In our case, this means running multiple samples for an ensemble concurrently, and reaping certain performance benefits. We demonstrate the effectiveness of these approaches here as a prelude to introducing them into ACME.
Geoscientific Model Development
This article discusses the problem of identifying extreme climate events such as intense storms within large climate data sets. The basic storm detection algorithm is reviewed, which splits the problem into two parts: a spatial search followed by a temporal correlation problem. Two specific implementations of the spatial search algorithm are compared: the commonly used grid point search algorithm is reviewed, and a new algorithm called Stride Search is introduced. The Stride Search algorithm is defined independently of the spatial discretization associated with a particular data set. Results from the two algorithms are compared for the application of tropical cyclone detection, and shown to produce similar results for the same set of storm identification criteria. Differences between the two algorithms arise for some storms due to their different definition of search regions in physical space. The physical space associated with each Stride Search region is constant, regardless of data resolution or latitude, and Stride Search is therefore capable of searching all regions of the globe in the same manner. Stride Search's ability to search high latitudes is demonstrated for the case of polar low detection. Wall clock time required for Stride Search is shown to be smaller than a grid point search of the same data, and the relative speed up associated with Stride Search increases as resolution increases.
The Department of Energy’s (DOE) Biological and Environmental Research project, “Water Cycle and Climate Extremes Modeling” is improving our understanding and modeling of regional details of the Earth’s water cycle. Sandia is using high resolution model behavior to investigate storms in the Arctic.
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