Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “discretization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

ASGarD: Adaptive Sparse Grid Discretization

Many areas of science exhibit physical processes that are described by high dimensional partial differential equations (PDEs), e.g., the 4D, 5D and 6D models describing magnetized fusion plasmas, models describing quantum chemistry, or derivatives pricing. Such problems are affected by the so-called “curse of dimensionality” where the number of degrees of freedom (or unknowns) required to be solved for scales as N D where N is the number of grid points in any given dimension D. A simple, albeit naive, 6D example is demonstrated in the left panel of Figure 1. With N = 1000 grid points in each dimension, the memory required just to store the solution vector, not to mention forming the matrix required to advance such a system in time, would exceed an exabyte - and also the available memory on the largest of supercomputers available today. The right panel of Figure 1 demonstrates potential savings for a range of problem dimensionalities and grid resolution. While there are methods to simulate such high-dimensional systems, they are mostly based on Monte-Carlo methods, which rely on a statistical sampling such that the resulting solutions include noise. Since the noise in such methods can only be reduced at a rate proportional to $\sqrt{N_p}$ where N p is the number of Monte-Carlo samples, there is a need for continuum, or grid/mesh-based methods for high-dimensional problems, which both do not suffer from noise and bypass the curse of dimensionality. We present a simulation framework that provides such a method using adaptive sparse grids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Discrete Measurements of the Least Horizontal Principal Stress from Core Data: An Application of Viscoelastic Stress Relaxation

Summary The emerging Paradox Oil Play in southeastern Utah is among the most significant unconventional plays in the western USA. The mean total undiscovered oil resources within just the Pennsylvanian Cane Creek interval of the Paradox Basin are believed to exceed 215 million barrels. However, to date, less than 5% (~9 million barrels) of the total Cane Creek resource has been produced from fewer than 40 wells, and only approximately one-half of those are horizontal wells. More than 95% of production is from the central Cane Creek Unit (CCU). Natural fractures are a key feature of many production wells, but stimulation by induced hydraulic fractures is not consistently successful. We hypothesize that more effective production in this play will rely on better fundamental characterization, especially on better quantification of the state of stress. Approximately 110 ft of core, well logs, and a diagnostic fracture injection test (DFIT) were acquired from the State 16-2 well within the CCU. With these data, we applied two methods to constrain and clarify the state of stress. The first technique, the Simpson’s coefficient method, provides lower bounds on the two horizontal principal stresses and relies on only limited data. Alternatively, the viscoelastic stress relaxation (VSR) method is used to estimate the least horizontal principal stress, building on observations that principal stresses become more isotropic as the viscous behavior of a rock is more pronounced. Results of these two methods support the hypothesis that the state of stress in the CCU of the Paradox Basin is nearly lithostatic and isotropic. Other factors consistent with this hypothesis include high formation pore pressure, which tends to reduce the possible stress states by changing the frictional failure equilibrium; lack of induced fractures in the core, which should be present in the case of stress anisotropy; and interbedded halite layers, which given their high degree of ductility, probably lead to greater VSR for the entire sedimentary package.

Energy & Fuels↗
DOE OSTI2021

Performance Evaluation of Engineered Geothermal Systems Using Discrete Fracture Network Simulations

Electrical power production from geothermal energy has a solid record of success for permeable reservoirs such as The Geysers in northern California and geothermal systems in Iceland and New Zealand, among other places. Such permeable reservoirs, however, represent only a small fraction of the available heat energy in the earth’s shallow crust. Most of the available energy resides in rocks with insufficient permeability and storage to produce commercial volumes of heated fluids.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

CIS Project 22359, Final Technical Report. Discretized Posterior Approximation in High Dimensions

Our primary aim in this work is to understand how to efficiently obtain reliable uncertainty quantification in automatic learning algorithms with limited training datasets. Standard approaches rely on cross-validation to tune hyper parameters. Unfortunately, when our datasets are too small, holdout datasets become unreliable—albeit unbiased—measures of prediction quality due to the lack of adequate sample size. We should not place confidence in holdout estimators under conditions wherein the sample variance is both large and unknown. More poigniantly, our training experiments on limited data (Duersch and Catanach, 2021) show that even if we could improve estimator quality under these conditions, the typical training trajectory may never even encounter generalizable models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Discrete modeling of a transformer with ALEGRA

We report progress on a task to model transformers in ALEGRA using the “Transient Magnetics” option. We specifically evaluate limits of the approach resolving individual coil wires. There are practical limits to the number of turns in a coil that can be numerically modeled, but calculated inductance can be scaled to the correct number of turns in a simple way. Our testing essentially confirmed this “turns scaling” hypothesis. We developed a conceptual transformer design, representative of practical designs of interest, and that focused our analysis. That design includes three coils wrapped around a rectangular ferromagnetic core. The secondary and tertiary coils have multiple layers. The tertiary has three layers of 13 turns each; the secondary has five layers of 44 turns; the primary has one layer of 20 turns. We validated the turns scaling of inductance for simple (one-layer) coils in air (no core) by comparison to available independent calculations for simple rectangular coils. These comparisons quantified the errors versus reduced number of turns modeled. For more than 3 turns, the errors are <5%. The magnetic field solver failed to converge (within 5000 iterations) for >10 turns. Including the core introduced some complications. It was necessary to capture the core surfaces in thin grid sheaths to minimize errors in computed magnetic energy. We do not yet have quantitative benchmarks with which to compare, but calculated results are qualitatively reasonable.

42 ENGINEERING↗