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Recent Progress in OVERFLOW Convergence Improvements

Improvements have been made to the implicit symmetric successive overrelaxation algorithm in the OVERFLOW 2.3 structured, overset grid, computational fluid dynamics flow solver. These improvements, consisting of implicit boundary conditions, improved flux Jacobian linearizations, and CFL number ramping, are a series of evolutionary changes to the linear solver that have resulted in increased nonlinear convergence rates and faster time to solution. A series of test cases are presented that demonstrate the effect of the changes through comparison with the original SSOR path and other linear solver implementations within OVERFLOW.

Joseph M Derlaga↗

NASA NTRS2010

Focal Plane Geometry Characterization of the Kepler Mission

The Kepler Mission focal plane contains 42 charge-coupled device (CCD) photodetectors. Each CCD is composed of 2.2 million square pixels, 27 micrometers on a side, arranged in a grid of 2,200 columns by 1,044 rows. The science goals of the Kepler Mission require that the position of each CCD be determined with an accuracy of 0.1 pixels, corresponding to 2.7 micrometers or 0.4 seconds of arc, a level which is not achievable through pre-flight metrology. We describe a technique for determining the CCD positioning using images of the Kepler field of view (FOV) obtained in flight. The technique uses the fitted centroid row and column positions of 400 pre-selected stars on each CCD to obtain empirical polynomials which relate sky coordinates (right ascension and declination) to chip coordinates (row and column). The polynomials are in turn evaluated to produce constraints for a nonlinear model fit which directly determines the model parameters describing the location and orientation of each CCD. The focal plane geometry characterization algorithm is itself embedded in an iterative process which determines the focal plane geometry and the Pixel Response Function for each CCD in a self-consistent manner. In addition to the fully automated calculation, a person-in-the-loop implementation was developed to allow an initial determination of the geometry in the event of large misalignments, achieving a much looser capture tolerance for more modest accuracy and reduced automation.

ccd↗

DOE OSTI2010

Modeling of plasma turbulence and transport in the Large Plasma Device

Numerical simulation of plasma turbulence in the Large Plasma Device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky et al., Rev. Sci. Instrum. 62, 2875 (1991)] is presented. The model, implemented in the BOUndary Turbulence code [M. Umansky, X. Xu, B. Dudson et al., Contrib. Plasma Phys. 180, 887 (2009)], includes three-dimensional (3D) collisional fluid equations for plasma density, electron parallel momentum, and current continuity, and also includes the effects of ion-neutral collisions. In nonlinear simulations using measured LAPD density profiles but assuming constant temperature profile for simplicity, self-consistent evolution of instabilities and nonlinearly generated zonal flows results in a saturated turbulent state. Comparisons of these simulations with measurements in LAPD plasmas reveal good qualitative and reasonable quantitative agreement, in particular in frequency spectrum, spatial correlation, and amplitude probability distribution function of density fluctuations. For comparison with LAPD measurements, the plasma density profile in simulations is maintained either by direct azimuthal averaging on each time step, or by adding particle source/sink function. The inferred source/sink values are consistent with the estimated ionization source and parallel losses in LAPD. These simulations lay the groundwork for more a comprehensive effort to test fluid turbulence simulation against LAPD data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Notes on the ExactPack Implementation of the DSD Explosive Arc Solver

It has been shown above that the discretization scheme implemented in the ExactPack solver for the DSD Explosive Arc equation is consistent with the Explosive Arc PDE. In addition, a stability analysis has provided a CFL condition for a stable time step. Together, consistency and stability imply convergence of the scheme, which is expected to be close to first-order in time and second-order in space. It is understood that the nonlinearity of the underlying PDE will affect this rate somewhat.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Numerical simulation of a thermodynamically consistent four‐species tumor growth model

We develop a thermodynamically consistent four‐species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction‐diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse‐interface models. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce. A time‐stepping algorithm is then presented for this system, which is shown to be first order accurate and energy gradient stable. The results of an array of numerical experiments are presented, which demonstrate a wide range of solutions produced by various choices of model parameters.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Intensity dependent spread processor and workstation

The Intensity Dependent Spread (IDS) is an adaptive algorithm which is modified according to the local intensity in the scene. (This results in a nonlinear process which cannot take advantage of rather nice linear transform methods.) The computation is similar to a neural net whereby intensity information is moving from each input pixel to a set of surrounding output pixels in a manner described by Cornsweet and Yellott. A prototype of a very large scale integration IDS processor is being developed and implemented in a workstation environment. The workstation consists of a SUN 3/260 and a DATACUBE pipeline processor. The IDS prototype is a board set which operates in the DATA CUBE processor. The SUN 3/260 performs control, background processing, IDS simulation and image display functions.

Westrom, George↗

DOE OSTI2014

Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow

This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier-Stokes equations and permits higher resolution studies of the dynamical system associated with the stochastic structural stability theory (S3T) model, which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented by reducing a DNS code so that it retains only the RNL dynamics. Comparisons of turbulence arising from DNS and RNL simulations demonstrate that the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivate use of the RNL/S3T framework for further study of wall-turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Graph-Based Representations and Applications to Process Simulation

Rapid and robust convergence of a process flowsheet is critical to enable large-scale simulations that address core scientific questions related to process design, optimization, and sustainability. However, due to the highly coupled and nonlinear nature of chemical processes, efficiently solving a flowsheet remains a challenge. In this work, we show that graph representations of the underlying physical phenomena in unit operations may help identify potential avenues to systematically reformulate the network of equations and enable more robust topology-based convergence of flowsheets. To this end, we developed graph abstractions of the governing equations of vapor-liquid and liquid-liquid equilibrium separation equipment. These graph abstractions consist of a mesh of interconnected variable nodes and equation nodes that are systematically generated through PhenomeNode, a new open-source library in Python developed in this study. We show that partitioning the graph into separate mass, energy, and equilibrium subgraphs can help decouple nonlinearities and guide decomposition algorithms. By employing the graph abstraction on an industrial separation process for separating glacial acetic acid from water, we implemented a new block decomposition scheme in BioSTEAM and demonstrated that this can accelerate convergence over a traditional sequential modular approach.

Distillation↗

DOE OSTI2014

The Heuristic Static Load-Balancing Algorithm Applied to the Community Earth System Model

We propose to use the heuristic static loadbalancing (HSLB) algorithm for solving load-balancing problems in the Community Earth System Model (CESM), a climate model, using fitted benchmark data as an alternative to the current manual approach. The problem of allocating the optimal number of CPU cores to CESM components is formulated as a mixed-integer nonlinear optimization problem which is solved by using an optimization branch-and-bound solver implemented in the MINLP package MINOTAUR. The key feature of the branch-and- bound method is that it guarantees to provide an optimal solution or show that none exists. Our algorithm was tested for the 1 degrees and 1/8 degrees resolution simulations on 32,768 nodes (131,072 cores) of IBM Blue Gene/P where we consistently achieved well load-balanced results. This work is a part of a broader effort to eliminate the need for manual tuning of the code for each platform and simulation type, improve the performance and scalability of CESM, and develop automated tools to achieve these goals.

Alekseev, Yury↗

DOE OSTI2021

Self-consistent simulation of resistive kink instabilities with runaway electrons

A new fluid model for runaway electron simulation based on fluid description is introduced and implemented in the magnetohydrodynamics code M3D-C1, which includes self-consistent interactions between plasma and runaway electrons. The model utilizes the method of characteristics to solve the continuity equation for the runaway electron density with large convection speed, and uses a modified Boris algorithm for pseudo particle pushing. The model was employed to simulate magnetohydrodynamics instabilities happening in a runaway electron final loss event in the DIII-D tokamak. Nonlinear simulation reveals that a large fraction of runaway electrons get lost to the wall when kink instabilities are excited and form stochastic field lines in the outer region of the plasma. Plasma current converts from runaway electron current to Ohmic current, and get pinched at the magnetic axis. Here, given the good agreement with experiment, the simulation model provides a reliable tool to study macroscopic plasma instabilities in existence of runaway electron current, and can be used to support future studies of runaway electron mitigation strategies in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2010

Nonlinear acceleration of SN transport calculations

The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Detecting Weak Coupling of Quantum Systems with a Nonequilibrium Fano Resonance

A critical aspect of quantum mechanics is the nonlocal nature of the wavefunction, a characteristic that may yield unexpected coupling of nominally-isolated systems. The capacity to detect this coupling can be vital in many situations, especially those in which its strength is weak. In this work we address this problem in the context of mesoscopic physics, by implementing an electron-wave realization of a Fano interferometer using pairs of coupled quantum point contacts (QPCs). Within this scheme, the discrete level required for a Fano resonance is provided by pinching off one of the QPCs, thereby inducing the formation of a quasi-bound state at the center of its self-consistent potential barrier. Using this system, we demonstrate a form of $\textit{nonequilibrium}$ Fano resonance (NEFR), in which nonlinear electrical biasing of the interferometer gives rise to pronounced distortions of its Fano resonance. Our experimental results are captured well by a quantitative theoretical model, which considers a system in which a standard two-path Fano interferometer is coupled to an additional, $\textit{intruder}$, continuum. According to this theory, the observed distortions in the Fano resonance arise $\textit{only}$ in the presence of coupling to the intruder, indicating that the NEFR provides a sensitive means to infer the presence of weak coupling between mesoscopic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Semi-analytical sensitivity analysis for nonlinear transient problems

Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; however, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

42 ENGINEERING↗

DOE OSTI2023

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use data sets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (a) a form of Nonlinear Vector Autoregression (NVAR), and (b) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi-Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures.

58 GEOSCIENCES↗

DOE OSTI2022

Femtosecond-Terawatt Hard X-Ray Pulse Generation with Chirped Pulse Amplification on a Free Electron Laser

Advances of high intensity lasers have opened up the field of strong field physics and led to a broad range of technological applications. Recent x ray laser sources and optics development makes it possible to obtain extremely high intensity and brightness at x ray wavelengths. In this paper, we present a system design that implements chirped pulse amplification for hard x ray free electron lasers. Numerical modeling with realistic experimental parameters show that near-transform-limit single-femtosecond hard x ray laser pulses with peak power exceeding 1 TW and brightness exceeding 4×10 35 s -1 mm -2 mrad -2 0.1\%bandwdith -1 can be consistently generated. In conclusion, realization of such beam qualities is essential for establishing systematic and quantitative understanding of strong field x-ray physics and nonlinear x ray optics phenomena.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Fourth Generation MPDV and MBR at DARHT

A new experimental setup for diagnosing hydrotest performance was designed, built, and implemented at DARHT. The setup consists of 128 points of fourth generation (Gen4) multiplexed photonic Doppler velocimetry (MPDV) and 128 separate points of modulation based ranging (MBR) to serve as a direct complement to the MPDV. The diagnostics were designed to overcome limitations in the third generation of the MPDV diagnostic that limited laser launch power to ~10 mW per point. As the main failure mechanism identified in the third generation MPDV system arose from stimulated Brillouin scattering, a nonlinear optical phenomenon inherent in standard single mode fiber, the fourth generation MPDV system reduced the number of time-multiplexed channels by a factor of two. This has allowed laser launch power to be increased to as much as 200 mW per channel which is a 20 times increase in the signal to noise ratio (SNR) as compared with the third generation system. This document will first discuss the previous limitations and describe the design of the system. This will be followed by the results of a simple flyer plate experiment used to demonstrate the improved SNR as well as calibrate the phase errors in the system that MBR is sensitive to.

42 ENGINEERING↗

DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1989

Experimental studies of adaptive structures for precision performance

An experimental study was made of the adaptive structure concept. Experimental data were obtained for a three-longeron, thirteen-bay truss-type test structure. This test structure can be softly suspended as well as rigidly clamped at the central bay. The load-carrying active member consists of a stack of concentric piezoelectric wafers, an eddy current displacement sensor, and a strain gage force sensor. A bridge (or compound) feedback technique developed in communication engineering is applied to the problem of active damping augmentation in adaptive structures. Using collocated force and velocity feedback around the active member, a desired output mechanical impedance can be implemented to maximize energy absorption by the active members. In addition, large gains can be implemented to linearize the active member's nonlinear behavior. Good agreements with linear finite element analysis was found for both static and dynamic structural responses. An 11 percent damping in the first bending mode was demonstrated in the closed-loop damping experiment.

Chen, G.-S.↗