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At least 1,261 records · Page 70

Sensitive parameter identification and uncertainty quantification for the stability of pipeline conveying fluid

In this study, several uncertainty quantification and sensitivity analysis methods are used to determine the most sensitive geometric and material input parameters of a cantilevered pipeline conveying fluid when uncertainty is introduced to the system at the onset of instability. The full nonlinear equations of motion are modeled using the extended Hamilton’s principle and then discretized using Galerkin’s method. A parametric study is first performed, and the Morris elementary effects are calculated to obtain a preliminary understanding of how the onset speed changes when each parameter is introduced to a ± 5% uncertainty. Then, four different input uncertainty distributions, mainly, uniform and Gaussian distribution, are chosen to investigate how input distributions affect uncertainty in the output. A convergence analysis is used to determine the number of samples needed to maintain simulation accuracy while saving the most computational time. Then, Monte Carlo simulations are run, and the output distributions for each input distribution at ± 1%, ± 3% and ± 5% input uncertainty range are found and discussed. Additionally, the Pearson correlation coefficients are evaluated for different uncertainty ranges. A final Monte Carlo study is performed in which single parameters are held constant while all others still have uncertainty. Overall, the flow speed at the onset of instability is the most sensitive to changes in the outer diameter of the pipe.

36 MATERIALS SCIENCE↗

High-performance finite elements with MFEM

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. Furthermore, this paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy’s Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED).

97 MATHEMATICS AND COMPUTING↗

Single Grid Error Estimation for Neutron Transport Solvers

The method of nearby problems (MNP) is a solution verification technique that does not require the use of multiple spatial grids. To estimate spatial discretization error without requiring a high-fidelity spatial grid, an analytical curve fit is interpolated from the numerical solution. The residual between the curve fit solution and numerical solution is calculated and added as an additional source term to the governing equation. The nearby solution is estimated using the updated source term and boundary conditions to remain consistent with the curve fit interpolation. The nearby solution can be compared to the curve fit solution as a discretization error estimation while using a single spatial grid. Without the use of higher fidelity spatial grids, the MNP is able to approximate the spatial discretization error, a facet of solution verification. The application of the method of nearby problems is presented for one- and two-dimensional neutron transport problems for both fixed source and criticality problems on the spatial variable. The fixed source results demonstrate the effectiveness of nearby problems for spatial error identification using the discrete ordinates method. Criticality results are shown to identify area of high spatial error for the C5G7 problem as well as for the discrete ordinates solver. A novel approach of combining the capabilities of Monte Carlo with the discrete ordinates nearby problems is presented for one- and two-dimensional fixed source problems. In conclusion, the MNP demonstrates its effectiveness at identifying spatial error on a single structured grid with a wide variety of neutron transport problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Enabling Predictive Simulation and UQ of Complex Multiphysics PDE Systems by the Development of Goal-Oriented Variational Sensitivity Analysis and A Posteriori Error Estimation Methods

It was demonstrated that a posteriori analyses in general and in particular one that uses adjoint methods can accurately and efficiently compute numerical error estimates and sensitivity for critical Quantities of Interest (QoIs) that depend on a large number of parameters. Activities include: analysis and implementation of several time integration techniques for solving system of ODEs as typically obtained from spatial discretization of PDE systems; multirate integration methods for ordinary differential equations; formulation and analysis of an iterative multi-discretization Galerkin finite element method for multi-scale reaction-diffusion equations; investigation of an inexpensive postprocessing technique to estimate the error of finite element solution of the second-order quasi-linear elliptic problems measured in some global metrics; investigation of an application of the residual-based a posteriori error estimates to symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems; a posteriori analysis of explicit time integrations for system of linear ordinary differential equations; derivation of accurate a posteriori goal oriented error estimates for a user-defined quantity of interest for two classes of first and second order IMEX schemes for advection-diffusion-reaction problems; Postprocessing finite element solution; and A Bayesian Framework for Uncertain Quantification of Porous Media Flows.

97 MATHEMATICS AND COMPUTING↗

Simulation and Comparison of Particle Injection in an Indoor Environment Using the Species Transport and Discrete Phase Models

In simulating fluid/solid-particle multiphase -flows, various methods are available. One approach is the combined Euler-Lagrange method, which simulates the fluid phase flow in the Eulerian framework and the discrete phase (particle) motion in the Lagrangian framework simultaneously. The Lagrangian approach, where particle motion is determined by the current state of the fluid phase flow, is also called the discrete phase model (DPM), in the context of numerical flow simulation. In this method, the influence of the particle motions on the fluid flow can be included (two-way interactions) but are more commonly excluded (one-way interactions, when the discrete phase concentration is dilute. The other approach is to treat the particle number concentration as a continuous species, a necessarily passive quantity determined by the fluid flow, with no influences from the particles on the fluid flow (one-way interactions only), except to the extent the discrete phase “continuum” alters the overall fluid properties, such as density. In this paper, we compare these two methods with experimental data for an indoor environmental chamber. The effects of injection particle numbers and the related boundary conditions are investigated. In the Euler-Lagrange interaction or DPM model for incompressible flow, the Eulerian continuous phase is governed by the Reynolds-averaged N-S (RANS) equations. The motions of particles are governed by Newton’s second law. The effects of particle motions are communicated to the continuous phase through a force term in the RANS equations. The second formulation is a pure Eulerian type, where only the particle-number concentration is addressed, rather than the motion of each individual particle. The fluid flow is governed by the same RANS equations without the particle force term. The particle-number concentration is simulated by a species transport equation. Comparisons among the models and with experimental and literature data are presented. Particularly, results with different numbers of released particles in the DPM will be investigated.

computational fluid dynamics↗

An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by nonconvex immersed bodies, multiply connected domains, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the immersed solid bodies, reducing computational cost and enabling simulations with nonconvex bodies that could not be discretized with previous immersed interface methods. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, allowing for simulations with multiply connected domains and outflow boundaries that have challenged other immersed interface vortex methods. We also explore novel methods for recovering time-dependent pressure distributions on immersed bodies within a vorticity-based method and present a novel control volume formulation for recovering aerodynamic moments from only the vorticity and velocity fields. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.

97 MATHEMATICS AND COMPUTING↗

Efficient algorithms for semiclassical instanton calculations based on discretized path integrals

Path integral instanton method is a promising way to calculate the tunneling splitting of energies for degenerated two state systems. In order to calculate the tunneling splitting, we need to take the zero temperature limit, or the limit of infinite imaginary time duration. In the method developed by Richardson and Althorpe [J. Chem. Phys. 134, 054109 (2011)], the limit is simply replaced by the sufficiently long imaginary time. In the present study, we have developed a new formula of the tunneling splitting based on the discretized path integrals to take the limit analytically. We have applied our new formula to model systems, and found that this approach can significantly reduce the computational cost and gain the numerical accuracy. We then developed the method combined with the electronic structure calculations to obtain the accurate interatomic potential on the fly. We present an application of our ab initio instanton method to the ammonia umbrella flip motion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Error analysis of numerical methods for thick diffusive neutron transport problems on Shishkin mesh

A thin layer will develop at the boundary if the incoming angular flux is anisotropic in thick diffusive neutron transport problems. Solving such singularly perturbed problems, which have non-smooth solutions with singularity near the boundary, is computationally challenging. Standard finite difference schemes on a uniform mesh cannot yield ε-uniform convergence, where ε is a small parameter, while it can be achieved on a suitable piecewise-uniform Shishkin mesh. We present a formal error analysis of the diamond difference (DD) method and step difference (SD) method for solving the S{sub N} neutron transport equation. The analysis can be extended to other finite difference methods. Numerical results are presented to confirm the error estimates and the advantages of the Shishkin mesh. (author)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Electromagnetic Scattering by Discrete Random Media Illuminated by a Gaussian Beam II: Solution of the Radiative Transfer Equation

In this paper, we present numerical methods for solving the phenomenological scalar radiative transfer equation for a discrete random medium illuminated by a Gaussian beam. These rely on the Fourier transform method for the horizontal variables and the discrete ordinate method with matrix exponential for solving the underlying one-dimensional radiative transfer equation in the wavenumber domain. The problem of a Gaussian beam at oblique and normal incidence, as well as, the searchlight problem are treated. A complete description of the methods and the numerical algorithms is provided.

Gaussian beam↗

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

42 ENGINEERING↗

Computation of Wave Loads under Multidirectional Sea States for Floating Offshore Wind Turbines: Preprint

This paper focuses on the analysis of a floating wind turbine under multidirectional wave loading. Special attention is given to the different methods used to synthesize the multidirectional sea state. This analysis includes the double-sum and single-sum methods, as well as an equal-energy discretization of the directional spectrum. These three methods are compared in detail, including the ergodicity of the solution obtained. From the analysis, the equal-energy method proved to be the most computationally efficient while still retaining the ergodicity of the solution. This method was chosen to be implemented in the numerical code FAST. Preliminary results on the influence of these wave loads on a floating wind turbine showed significant additional roll and sway motion of the platform.

17 WIND ENERGY↗

OPTIMIZED MULTI-FREQUENCY SPECTRA FOR APPLICATIONS IN RADIATIVE FEEDBACK AND COSMOLOGICAL REIONIZATION

The recent implementation of radiative transfer algorithms in numerous hydrodynamics codes has led to a dramatic improvement in studies of feedback in various astrophysical environments. However, because of methodological limitations and computational expense, the spectra of radiation sources are generally sampled at only a few evenly spaced discrete emission frequencies. Using one-dimensional radiative transfer calculations, we investigate the discrepancies in gas properties surrounding model stars and accreting black holes that arise solely due to spectral discretization. We find that even in the idealized case of a static and uniform density field, commonly used discretization schemes induce errors in the neutral fraction and temperature by factors of two to three on average, and by over an order of magnitude in certain column density regimes. The consequences are most severe for radiative feedback operating on large scales, dense clumps of gas, and media consisting of multiple chemical species. We have developed a method for optimally constructing discrete spectra, and show that for two test cases of interest, carefully chosen four-bin spectra can eliminate errors associated with frequency resolution to high precision. Applying these findings to a fully three-dimensional radiation-hydrodynamic simulation of the early universe, we find that the H II region around a primordial star is substantially altered in both size and morphology, corroborating the one-dimensional prediction that discrete spectral energy distributions can lead to sizable inaccuracies in the physical properties of a medium, and as a result, the subsequent evolution and observable signatures of objects embedded within it.

79 ASTRONOMY AND ASTROPHYSICS↗

Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations

A fast multigrid solver for the steady incompressible Navier-Stokes equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Numerical solutions are shown for flow over a flat plate and a Karman-Trefftz airfoil. Using collective Gauss-Seidel line relaxation in both the vertical and horizontal directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of a Runge-Kutta based multigrid method.

Swanson, R. C.↗

Control of matrix converters using machine learning

A method of controlling a matrix converter system is provided. The method includes receiving an operating condition and consulting a trained Q-data structure for reward values associated with respective switching states of the switching matrix for an operating state that corresponds to the operating condition. The Q-data structure is trained using Q-learning to map a reward value predicted for respective switching states to respective discrete operating states. The method further includes sorting the reward values predicted for the respective switching states mapped to the operating state that corresponds to the operating condition, selecting a subset of the set of the mappings as a function of a result of sorting the reward values associated with the switching states of the operating state, evaluating each switching state included in the subset, and selecting an optimal switching state for the operating condition based on a result of evaluating the switching states of the subset.

Chamie, Mahmoud El↗

Sampling rare fluctuations of discrete-time Markov chains

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. Here, we focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

79 ASTRONOMY AND ASTROPHYSICS↗

Cross-Combined Composite Sampling Designs for Identification of Elevated Regions

Analyzing soils for contaminants can be costly. Generally, discrete samples are gathered from within a study area, analyzed by a laboratory and the results are used in a site-specific statistical analysis. Because of the heterogeneities that exist in soil samples within study areas, a large amount of variability and skewness may be present in the sample population. This necessitates collecting a large number of samples to obtain reliable inference on the mean contaminant concentration and to understand the spatial patterns for future remediation. Composite or Incremental sampling is a commonly applied method for gathering multiple discrete samples and physically combining them, such that each combination of discrete samples requires a single laboratory analysis, which reduces cost and can improve the estimates of the mean concentration. While incremental sampling can reduce cost and improve mean estimates, current implementations do not readily facilitate the characterization of spatial patterns or the detection of elevated regions within study areas. The methods we present in this work provide efficient estimation and inference for the mean contaminant concentration over the entire spatial area and enable the identification of high contaminant regions within the area of interest. We develop sample design methodologies that explicitly define the characteristics of these designs (such as sample grid layout) and quantify the number of incremental samples that must be obtained under a design criteria to control false positive and false negative (Type I and II) decision errors. We present the sample design theory and specifications as well as results on simulated and real data.

Hathaway, John E↗