LLNL Analytical Methods Update [Slides]
Abstract not provided.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
SEARCH · Engineering Papers
Results for “Mathematical methods”
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.
Achieving Realistic Runoff in the Western United States with a Land Surface Model Forced by Dynamically Downscaled Meteorology
Abstract In this study, we calibrate a regional climate model’s (RCM) underlying land surface model (LSM). In addition to providing a realistic representation of runoff across the hydroclimatically diverse western United States, this is done to take advantage of the RCM’s ability to physically resolve meteorological forcing data in ungauged regions, and to prepare the calibrated hydrologic model for tight coupling, or the ability to represent land surface–atmosphere interactions, with the RCM. Specifically, we use a 9-km resolution meteorological forcing dataset across the western United States, from the fifth generation ECMWF Reanalysis (ERA5) downscaled by the Weather Research Forecasting (WRF) regional climate model, as an offline forcing for Noah-Multiparameterization (Noah-MP). We detail the steps involved in producing an LSM capable of accurately representing runoff, including physical parameterization selection, parameter calibration, and regionalization to ungauged basins. Based on our model evaluation from 1954 to 2021 for 586 basins with daily natural streamflow, the streamflow bias is reduced from 24.2% to 4.4%, and the median daily Nash–Sutcliffe efficiency (NSE) is improved from 0.12 to 0.36. When validating against basins with monthly natural streamflow data, we obtain a similar reduction in bias and a median monthly NSE improvement from 0.18 to 0.56. In this study, we also discover the optimal setup when using a donor-basin method to regionalize parameters to ungauged basins, which can vary by 0.06 NSE for unique designs of this regionalization method. Significance Statement This study provides useful guidance for improving a land surface model to accurately represent runoff across a spatially extensive and hydroclimatically diverse region (the western United States). The land surface model is updated to represent runoff more accurately at gauged basins, and then additionally updated for basins without observational data using a mathematical approach called the donor-basin method. We make use of a regional climate model’s reanalysis-derived meteorological data and its underlying land surface model to achieve realistic runoff. The calibrated land surface model can thus be tightly coupled in subsequent studies in a manner that should more accurately reflect runoff conditions. Findings from this study will serve as a useful reference for the atmospheric (and hydrologic) modeling communities and their ability to represent large-scale hydrology accurately.
Meteorology & Atmospheric Sciences↗
Optimized mirror shape tuning using beam weightings based on distance, angle of incidence, reflectivity, and power
For glancing-incidence optical systems, such as short-wavelength optics used for nano-focusing, incorporating physical factors in the calculations used for shape optimization can improve performance. Wavefront metrology, including the measurement of a mirror's shape or slope, is routinely used as input for mirror figure optimization on mirrors that can be bent, actuated, positioned, or aligned. Modeling shows that when the incident power distribution, distance from focus, angle of incidence, and the spatially varying reflectivity are included in the optimization, higher Strehl ratios can be achieved. Following the works of Maréchal and Mahajan, optimization of the Strehl ratio (for peak intensity with a coherently illuminated system) occurs when the expectation value of the phase error's variance is minimized. We describe an optimization procedure based on regression analysis that incorporates these physical parameters. This approach is suitable for coherently illuminated systems of nearly diffraction-limited quality. Mathematically, this work is an enhancement of the methods commonly applied for ex situ alignment based on uniform weighting of all points on the surface (or a sub-region of the surface). It follows a similar approach to the optimization of apodized and non-uniformly illuminated optical systems. Significantly, it reaches a different conclusion than a more recent approach based on minimization of focal plane ray errors.
47 OTHER INSTRUMENTATION↗
An investigation of Newton-Sketch and subsampled Newton methods
Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. In this work, we study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not been investigated in the optimization literature. Additionally, our study focuses on practical versions of the two methods in which the resulting linear systems of equations are solved approximately, at every iteration, using an iterative solver. The advantages of using the conjugate gradient method vs. a stochastic gradient iteration are revealed through a set of numerical experiments, and a complexity analysis of the Hessian subsampling method is presented.
97 MATHEMATICS AND COMPUTING↗
Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks
We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.
97 MATHEMATICS AND COMPUTING↗
Effective computation of stochastic protein kinetic equation by reducing stiffness via variable transformation
The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.
97 MATHEMATICS AND COMPUTING↗
Assessing the Impact of Sensitivity/Uncertainty Selection Criteria on Computational Bias Prediction [Slides]
This presentation on assessing the impact of sensitivity/uncertainty selection criteria on computational bias prediction starts with providing a motivation and scope. This presentation then gives the selection criteria description with the method and application. This presentation finishes with results, conclusions, and future work.
97 MATHEMATICS AND COMPUTING↗
Quasi-periodic travelling gravity–capillary waves
We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.
97 MATHEMATICS AND COMPUTING↗
A simple finite element method for linear hyperbolic problems
Not Available
97 MATHEMATICS AND COMPUTING↗
The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects
In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.
Physics↗
COPTRAN - A method of optimum communication systems design
Single set of mathematical expressions describes system cost and probability of error of data transmission in terms of four basic parameters in the link equation. A Lagrange multiplier sets up equations whose solutions yield the optimum values for system design considerations and weight and cost values.
Brinkman, K. L.↗
Point-Mass Aircraft Trajectory Prediction Using a Hierarchical, Highly-Adaptable Software Design
A highly adaptable and extensible method for predicting four-dimensional trajectories of civil aircraft has been developed. This method, Behavior-Based Trajectory Prediction, is based on taxonomic concepts developed for the description and comparison of trajectory prediction software. A hierarchical approach to the "behavioral" layer of a point-mass model of aircraft flight, a clear separation between the "behavioral" and "mathematical" layers of the model, and an abstraction of the methods of integrating differential equations in the "mathematical" layer have been demonstrated to support aircraft models of different types (in particular, turbojet vs. turboprop aircraft) using performance models at different levels of detail and in different formats, and promise to be easily extensible to other aircraft types and sources of data. The resulting trajectories predict location, altitude, lateral and vertical speeds, and fuel consumption along the flight path of the subject aircraft accurately and quickly, accounting for local conditions of wind and outside air temperature. The Behavior-Based Trajectory Prediction concept was implemented in NASA's Traffic Aware Planner (TAP) flight-optimizing cockpit software application.
Karr, David A.↗
Whitepaper on Uncertainty Quantification for MPACT
The MPACT code provides the ability to perform high-fidelity deterministic calculations to obtain a wide variety of detailed results for very complex reactor core models. However, MPACT currently does not have the capability to propagate the effects of input data uncertainties to provide uncertainties in the calculated results. This white paper discusses a potential method for MPACT uncertainty quantification (UQ) based on stochastic sampling.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Gray-Box Modeling for Distribution Systems With Inverter-Based Resources: Integrating Physics-Based and Data-Driven Approaches
Here, in this paper, we develop a novel gray-box modeling approach for distribution systems with inverter-based resources (IBRs). The proposed gray-box modeling method aims to improve estimation accuracy by taking advantages of both physics-based (white-box) and data-driven (black-box) modeling approaches. To this end, we utilize partial physical knowledge of the system, including the inverters’ structures and control diagrams, as well as the equivalent network model simplified through Kron reduction. The white-box model containing unknown parameters is then constructed with mathematical equations and an optimization-based method is subsequently employed to identify these unknown parameters within the white-box model. Next, the graybox modeling framework is then constructed by embedding the output variables of the white-box model into the input vector of a black-box model (represented using a neural network). Finally, the black-box section is trained using the collected input-output datasets and the gray-box model is then obtained. Furthermore, case studies demonstrate that our gray-box modeling approach effectively improves estimation accuracy compared to purely physics-based or data-driven methods.
42 ENGINEERING↗
A Textbook for a First Course in Computational Fluid Dynamics
This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.
Zingg, D. W.↗
Aerodynamic sensitivity analysis methods for the compressible Euler equations
This study presents a mathematical formulation developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible 2D Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. The finite difference approach and the quasi-analytical approach are used to determine the aerodynamic sensitivity coefficients. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flowfield solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.
Baysal, Oktay↗
Using a meshless kernel-based method to solve the Black–Scholes variational inequality of American options
Under the Black–Scholes model, the value of an American option solves a free boundary problem which is equivalent to a variational inequality problem. Using positive definite kernels, we discretize the variational inequality problem in spatial direction and derive a sequence of linear complementarity problems (LCPs) in a finite-dimensional euclidean space. We use special kind of kernels to impose homogeneous boundary conditions and to obtain LCPs with positive definite coefficient matrices to guarantee the existence and uniqueness of the solution. The LCPs are then successfully solved iteratively by the projected SOR algorithm.
97 MATHEMATICS AND COMPUTING↗
VERA and VERA-EDU 3.5 Release Notes
The Virtual Environment for Reactor Applications components included in this distribution include selected computational tools and supporting infrastructure that solve neutronics, thermal-hydraulics, fuel performance, and coupled neutronics-thermal hydraulics problems. The infrastructure components provide a simplified common user input capability and provide for the physics integration with data transfer and coupled-physics iterative solution algorithms. Neutronics analysis can be performed for 2D lattices, 2D core and 3D core problems for pressurized water reactor geometries that can be used to calculate criticality and fission rate distributions by pin for input fuel compositions. MPACT uses the Method of Characteristics transport approach for 2D problems. For 3D problems, MPACT uses the 2D/1D method which uses 2D MOC in a radial plane and diffusion or SPn in the axial direction. MPACT includes integrated cross section capabilities that provide problem-specific cross sections generated using the subgroup methodology. The code can be executed both 2D and 3D problems in parallel to reduce overall run time. A thermal-hydraulics capability is provided with CTF (an updated version of COBRA-TF) that allows thermal-hydraulics analyses for single and multiple assemblies using the simplified VERA common input. This distribution also includes coupled neutronics/thermal-hydraulics capabilities to allow calculations using MPACT coupled with CTF. The VERA fuel rod performance component BISON calculates, on a 2D or 3D basis, fuel rod temperature, fuel rod internal pressure, free gas volume, clad integrity and fuel rod waterside diameter. These capabilities allow simulation of power cycling, fuel conditioning and deconditioning, high burnup performance, power uprate scoping studies, and accident performance. Input/Output capabilities include the VERA Common Input (VERAIn) script which converts the ASCII common input file to the intermediate XML used to drive all of the physics codes in the VERA Core Simulator (VERA-CS). VERA component codes either input the VERA XML format directly, or provide a preprocessor which can convert the XML into native input. VERAView is an interactive graphical interface for the visualization and engineering analyses of output data from VERA. The python-based software is easy to install and intuitive to use, and provides instantaneous 2D and 3D images, 1D plots, and alpha-numeric data from VERA multi-physics simulations. Testing within CASL has focused primarily on Westinghouse four-loop reactor geometries and conditions with example problems included in the distribution.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗