Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convergence analysis”

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 1,243 records · Page 69

Nonlinear grid error effects on numerical solution of partial differential equations

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Dey, S. K.↗

Preconditioned methods for solving the incompressible and low speed compressible equations

Acceleration methods are presented for solving the steady state incompressible equations. These systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state. The compressible equations in conservation form with slow flow are also considered. Two arbitrary functions, alpha and beta, are introduced in the general preconditioning. An analysis of this system is presented and an optimal value for beta is determined given a constant, alpha. It is further shown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed. Several generalizations to the compressible equations are presented which generalize previous results.

Turkel, E.↗

A layered abduction model of perception: Integrating bottom-up and top-down processing in a multi-sense agent

A layered-abduction model of perception is presented which unifies bottom-up and top-down processing in a single logical and information-processing framework. The process of interpreting the input from each sense is broken down into discrete layers of interpretation, where at each layer a best explanation hypothesis is formed of the data presented by the layer or layers below, with the help of information available laterally and from above. The formation of this hypothesis is treated as a problem of abductive inference, similar to diagnosis and theory formation. Thus this model brings a knowledge-based problem-solving approach to the analysis of perception, treating perception as a kind of compiled cognition. The bottom-up passing of information from layer to layer defines channels of information flow, which separate and converge in a specific way for any specific sense modality. Multi-modal perception occurs where channels converge from more than one sense. This model has not yet been implemented, though it is based on systems which have been successful in medical and mechanical diagnosis and medical test interpretation.

Josephson, John R.↗

Performance implications from sizing a VM on multi-core systems: A Data analytic application s view

In this paper, we present a quantitative performance analysis of data analytics applications running on multi-core virtual machines. Such environments form the core of cloud computing. In addition, data analytics applications, such as Cassandra and Hadoop, are becoming increasingly popular on cloud computing platforms. This convergence necessitates a better understanding of the performance and cost implications of such hybrid systems. For example, the very rst step in hosting applications in virtualized environments, requires the user to con gure the number of virtual processors and the size of memory. To understand performance implications of this step, we benchmarked three Yahoo Cloud Serving Benchmark (YCSB) workloads in a virtualized multi-core environment. Our measurements indicate that the performance of Cassandra for YCSB workloads does not heavily depend on the processing capacity of a system, while the size of the data set is critical to performance relative to allocated memory. We also identi ed a strong relationship between the running time of workloads and various hardware events (last level cache loads, misses, and CPU migrations). From this analysis, we provide several suggestions to improve the performance of data analytics applications running on cloud computing environments.

Lim, Seung-Hwan↗

EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on input and model uncertainties, while numerical errors were largely overlooked. Numerical errors can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration of discretization error is mainly due to the difficulty in estimating them. Accurate estimations of discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are difficult to achieve in existing codes. In this work, we will build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verification of spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated via case studies that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties.

42 ENGINEERING↗

Analysis of Slope Limiters on Irregular Grids

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the proper - ties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear programming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

Berger, Marsha↗

Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

36 MATERIALS SCIENCE↗

The Dynamics of Megafire Smoke Plumes in Climate Models: Why a Converged Solution Matters for Physical Interpretations

As the climate system warms, megafires have become more frequent with devastating effects. A byproduct of these events is the creation of smoke plumes that can rise into the stratosphere and spread across the globe where they reside for many months. To gain a deeper understanding of the plume dynamics, global climate simulations of a megafire were performed at a wide range of grid spacings from 2.0° down to 7 km, including a 7 km nonhydrostatic experiment. The analysis focuses on how the resolved dynamics affects the specification of the plume characteristics such as injection height and black carbon (BC) mass. Prior studies initialize the smoke plume at one or a few grid points and this is shown here to produce severely dissipative dynamics. In order to validate such simulations with observations, enhancements of the plume characteristics to offset the dissipation is necessary. Using a numerically converged simulation, sensitivity tests show that to approximate the observed stratospheric lifetime, a reduction in BC fraction by 50% is necessary for external mixtures. The vorticity dynamics of the plume is also analyzed with a Lagrangian budget to understand the mechanisms responsible for the evolution of a collocated anticyclonic vortex. The results can be distilled down into a simple conceptual model. As the plume rises, the air diverges at the top of the updraft where the largest concentrations of smoke are found. This divergence induces a dilution of the background cyclonic absolute vorticity producing an anticyclonic vortex. Vortex decay occurs from opposite arguments.

54 ENVIRONMENTAL SCIENCES↗

Transient Modeling and Simulation of a Generic Stable Salt Reactor

A SAM system-level model of a generic stable salt reactor has been developed to investigate thermal-hydraulic behavior and safety performance under steady and transient conditions. The model integrates information generated from a reactor physics analysis using PROTEUS and PERSENT, and a computation fluid dynamics (CFD) analysis using STAR-CCM+. A loose, iterative coupling scheme between PROTEUS and SAM is implemented to calculate the equilibrium power and temperature distributions in the steady-state critical core condition. The converged steady-state model is then used in PERSENT to calculate the four reactivity feedback temperature coefficients (Doppler, fuel density, coolant density, and core radial expansion) and kinetic parameters that are needed in SAM to model the temperature feedback effects in transient simulations. Within the fully enclosed liquid fuel pins, natural convection is the dominant heat transfer mechanism. The STAR-CCM+ model of the fuel pin considers conjugate heat transfer from the liquid fuel salt to the pin cladding and external reactor coolant. The CFD results of the axial and radial temperature profiles are used to empirically determine an effective fuel salt thermal conductivity in the SAM fuel pin model so that the temperatures predicted by the SAM model match as closely as possible the CFD results. In the central region of the fuel pin, the effective thermal conductivity is as high as similar to 60 times the physical fuel salt thermal conductivity. The whole-plant SAM model is then used to simulate an unprotected station blackout transient. The results of this simulation showed that the large negative fuel axial expansion reactivity feedback reduces fission power to similar to 2.4% nominal power. The core is cooled by natural circulation, which removes heat in the core to the emergency heat removal system, and ultimately, to the ambient. However, peak fuel salt and cladding temperatures can potentially reach as high as 1500 K, albeit briefly, if the shutdown mechanism fails to operate.

stable salt reactor; transient simulations; system↗

Analysis of regularized Navier-Stokes equations. I, II

A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence and uniqueness are established for two classes of generalized solutions. It is shown that the solution of this regularized system converges to the solution of the conventional Navier-Stokes equations for low Reynolds numbers. Particular attention is given to the structure of attractors characterizing the solutions. Both local and global invariant manifolds are found, and the regularity properties of these manifolds are analyzed.

Ou, Yuh-Roung↗

The Fusion Driven Rocket: Nuclear Propulsion through Direct Conversion of Fusion Energy

The future of manned space exploration and development of space depends critically on the creation of a dramatically more efficient propulsion architecture for in-space transportation. A very persuasive reason for investigating the applicability of nuclear power in rockets is the vast energy density gain of nuclear fuel when compared to chemical combustion energy. The Fusion Driven rocket (FDR) represents a revolutionary approach to fusion propulsion where the power source releases its energy directly into the propellant, not requiring conversion to electricity. It employs a solid lithium propellant that requires no significant tankage mass. The propellant is rapidly heated and accelerated to high exhaust velocity (> 30 km/s), while having no substantial physical interaction with the spacecraft thereby avoiding damage to the rocket and limiting both the thermal heat load and radiator mass. The key to achieving this stems from research at MSNW and the UW on the magnetically driven implosion of metal foils onto a magnetized plasma target to obtain fusion conditions. A logical extension of this work leads to a method that utilizes these metal shells (or liners) to not only achieve fusion conditions, but to serve as the propellant as well. Several low-mass, magnetically driven metal liners are inductively driven to converge radially and axially and form a thick blanket surrounding the target plasmoid and compress the plasmoid to fusion conditions. Virtually all of the radiant, neutron and particle energy from the plasma is absorbed by the encapsulating, thick metal blanket thereby isolating the spacecraft from the fusion. This energy, in addition to the intense Ohmic heating at peak magnetic field compression, is adequate to vaporize and ionize the metal blanket. The expansion of this hot, ionized metal propellant through a magnetically insulated nozzle produces high thrust at the optimal Isp. The energy from the fusion process, along with the waste heat, is thus utilized at very high efficiency. The basic scheme for FDR is illustrated and described in the report (see Fig. 2) The two most critical issues in meeting challenges introduced employing magneto-inertial fusion as the power source is driver efficiency and “stand-off” – the ability to isolate and protect fusion and thruster from the resultant fusion energy. By employing metal shells for compression, it is possible to produce the desired convergent motion inductively by inserting the metal sheets along the inner surface of cylindrical or conically tapered coils. Both stand-off and energy efficiency issues are solved by this arrangement. 3 This two year effort focused on achieving three key criteria for the Fusion Driven Rocket to move forward for technological development: (1) the physics of the FDR must be fully understood and validated, (2) the design and technology development for the FDR required for its implementation in space must be fully characterized, and (3) an in-depth analysis of the rocket design and spacecraft integration as well as mission architectures enabled by the FDR need to be performed. A subscale, laboratory liner compression test facility was assembled at the University of Washington Plasma Dynamics Laboratory with sufficient liner kinetic energy (~ 0.5 MJ) to reach conditions required for fusion breakeven conditions. Detailed experimental studies of the dynamic behavior of the driven liners as well as liner convergence and magnetic compression were performed. The development of both the 1D liner dynamics code and the full 3D ANSYS® liner calculations was achieved. The characterization of both the FDR and spacecraft as well as a design architecture analysis was conducted that included an examination of a wide range of mission architectures and destinations for which this fusion propulsion system would be enabling or critical. In particular a rapid, single launch manned Mars mission was developed.

Energy↗

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Chemistry↗

Estimating the density of states of frustrated spin systems

Abstract Estimating the density of states (DOS) of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. DOS estimation has also recently become an indispensable tool for the benchmarking of quantum annealers when these function as samplers. Some of the standard approaches suffer from a spurious convergence of the estimates to metastable minima, and these cases are particularly hard to detect. Here, we introduce a sampling technique based on population annealing enhanced with a multi-histogram analysis and report on its performance for spin glasses. We demonstrate its ability to overcome the pitfalls of other entropic samplers, resulting in some cases in large scaling advantages that can lead to the uncovering of new physics. The new technique avoids some inherent difficulties in established approaches and can be applied to a wide range of systems without relevant tailoring requirements. Benchmarking of the studied techniques is facilitated by the introduction of several schemes that allow us to achieve exact counts of the degeneracies of the tested instances.

Barash, Lev (ORCID:000000022298785X)↗

V&V of Residual Stress for GTS

Residual stresses induced during forging and welding can cause detrimental failure in reservoirs due to enhanced possibility of crack propagation. Therefore, reservoirs must be designed with yield strengths in a tight range. This report summarizes an effort to verify and validate a computational tool that was developed to aid in prediction of the evolution of residual stresses throughout the manufacturing process. The application requirements are identified and summarized in the context of the Predictive Capability Maturity Model (PCMM). The phenomena of interest that the model attempts to capture are discussed and prioritized using the Phenomena Identification and Ranking Table (PIRT) to identify any gaps in our approach. The fidelity of the modeling approach is outlined and details on the implementation and boundary conditions are provided. The code verification requirements are discussed and solution verification is performed, including a mesh convergence study on the series of modeling steps (forging, machining and welding). Validation activities are summarized, including validation of the displacements, residual stresses, recrystallization, yield strength and thermal history. A sensitivity analysis and uncertainty quantification are also performed to understand how variations in the manufacturing process affect the residual stresses.

42 ENGINEERING↗

Development of Automated Atom Probe Tomography capability to study the influence of applied voltage and laser power on the final apparent composition of the analyzed specimen

This study presents the development and implementation of an autonomous Bayesian optimization (BO) framework for controlling and optimizing experimental parameters in Atom Probe Tomography (APT). Using commercial silicon needle samples as a benchmark system, we demonstrate that BO can efficiently navigate the complex parameter space of voltage and laser power to achieve target charge state ratios (specifically Si + /(Si + +Si 2+ )) with minimal experimental evaluations. Our implementation integrates Gaussian Process modeling with the CAMECA atom probe control framework, enabling autonomous adjustment of experimental conditions in real-time. Results show that the algorithm successfully converges to target ratios under different scenarios: maintaining a reference ratio, increasing the ratio (favoring Si 1+ ), and decreasing the ratio (favoring Si 2+ ). The system adapts to specimen evolution during analysis, compensating for changes in apex geometry while maintaining optimization targets. This work establishes a proof of concept for AI-driven optimization in APT, addressing the traditional challenges of manual parameter tuning and paving the way for applications to more complex materials where compositional accuracy is critical.

36 MATERIALS SCIENCE↗

Techniques for generation of control and guidance signals derived from optical fields, part 2

The development is reported of a high resolution technique for the detection and identification of landmarks from spacecraft optical fields. By making use of nonlinear regression analysis, a method is presented whereby a sequence of synthetic images produced by a digital computer can be automatically adjusted to provide a least squares approximation to a real image. The convergence of the method is demonstrated by means of a computer simulation for both elliptical and rectangular patterns. Statistical simulation studies with elliptical and rectangular patterns show that the computational techniques developed are able to at least match human pattern recognition capabilities, even in the presence of large amounts of noise. Unlike most pattern recognition techniques, this ability is unaffected by arbitrary pattern rotation, translation, and scale change. Further development of the basic approach may eventually allow a spacecraft or robot vehicle to be provided with an ability to very accurately determine its spatial relationship to arbitrary known objects within its optical field of view.

Hemami, H.↗