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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations

A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ω pe Δt >>1, and Δx >> λ D ), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylov (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

brulilo, Version 0.x

brulilo is a Python package for building and evolving thermonuclear reaction networks, such as those used in astrophysical explosion calculations. It is very much a current work in progress, and much of the intended functionality is still under development. The main goal of brulilo is an easy-to-use code for quick calculations or post-processing, as well as a learning tool to test various implementations of solvers on both CPUs and GPUs. Currently, brulilo parses an input text file that specifies the reactions to be included in the network. The notation of the inputs are in the typical astrophysical notation; i.e. hydrogen burning to deuterium in the sun, "p + p + e --> d + neutrino", is given as "p(p,)d." Each reaction is added to a list comprising the reaction network, and once completed, the network contains a list of all isotopes and reactions involved. brulilo then parses publicly available nuclear data (binding energy, spin, partition function data, etc.) for each isotope from the WebNucleo group's data at nucleo.ces.clemson.edu. Fits to reaction rate data for each reaction are obtained from the publicly available data provided by the Joint Institute for Nuclear Astrophysics' Reaclib database. Reverse reactions are calculated from detailed balance. The reaction network then consists of a sparse system of mathematically stiff ordinary differential equations (ODEs). Physically, "stiffness" here means that there are some reaction rates that are occurring much faster than others; the ratio of the fast to slow often being greater than 10^15 in astrophysics. Numerical integration of such systems typically involves implicit integration schemes, which brulilo will leverage from the scientific computing Python package, Numpy, as well as implement its own. There has recently been work from researchers at Oak Ridge National Lab who have found good results from applying quasi-equilibrium and quasi-asymptotic conditions to the stiff system of ODEs, which effectively remove some of the stiffness and allow for efficient explicit integration techniques to be used. The original intent of brulilo was to implement these stiffness-alleviating techniques with explicit integrators and compare the performance to traditional implicit integrations of the full stiff system. This is still underway, as the code is very much in an alpha-release state. Furthermore, explicit integrators are often much easier to parallelize than their implicit counterparts. brulilo will implement parallelization of these techniques, leveraging both the Python implementation of MPI, mpi4py, as well as highly parallelized versions targeted at GPUs with PyOpenCL and/or PyCUDA.

Malone, Chris↗
DOE OSTI2019

NONLINEAR SOIL-STRUCTURE INTERACTION ANALYSIS USING CO-SIMULATION

Nonlinear soil-structure interaction (NLSSI) analysis methods are currently being developed at Idaho National Laboratory. Appendix B in ASCE (2016) includes a framework for performing NLSSI analysis. For NLSSI analysis to be widely implemented in industry, it is important to demonstrate that accurate response in dynamically loaded, nonlinear models can be achieved in an efficient manner. Both explicit and implicit dynamic solvers are applicable to NLSSI. When considering cpu time, an explicit dynamic solver is often desirable for large models with no features (e.g. small elements, stiff elements, or stiffness damping) that can drive the time step unreasonably small. An implicit dynamic solver may be desirable in models not well suited for an explicit solver. A further option is co-simulation where a portion of the model is run with an explicit dynamic solver and the rest of the model is run with an implicit dynamic solver. This study explores NLSSI examples where co-simulation could be the most cpu efficient modelling strategy.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2017

Improvement of the prediction of surface ozone concentration over conterminous U.S. by a computationally efficient second-order Rosenbrock solver in CAM4-Chem

The global chemistry-climate model (CAM4-Chem) overestimates the surface ozone concentration over the conterminous U.S. (CONUS). Reasons for this positive bias include emission, meteorology, chemical mechanism, and solver. In this study, we explore the last possibility by examining the sensitivity to the numerical methods for solving the chemistry equations. A second-order Rosenbrock (ROS-2) solver is implemented in CAM4-Chem to examine its influence on the surface ozone concentration and the computational performance of the chemistry program. Results show that under the same time step size (1800 s), statistically significant reduction of positive bias is achieved by the ROS-2 solver. The improvement is as large as 5.2 ppb in Eastern U.S. during summer season. The ROS-2 solver is shown to reduce the positive bias in Europe and Asia as well, indicating the lower surface ozone concentration over the CONUS predicted by the ROS-2 solver is not a trade-off consequence with increasing the ozone concentration at other global regions. In addition, by refining the time step size to 180 s, the first-order implicit solver does not provide statistically significant improvement of surface ozone concentration. It reveals that the better prediction from the ROS-2 solver is not only due to its accuracy but also due to its suitability for stiff chemistry equations. As an added benefit, the computation cost of the ROS-2 solver is almost half of first-order implicit solver. The improved computational efficiency of the ROS-2 solver is due to the reuse of the Jacobian matrix and lower upper (LU) factorization during its multistage calculation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem

In this paper, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Finally, marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms.

42 ENGINEERING↗
DOE OSTI2014

Massively parallel solvers for elliptic partial differential equations in numerical weather and climate prediction

The demand for substantial increases in the spatial resolution of global weather and climate prediction models makes it essential to use numerically efficient and highly scalable algorithms to solve the equations of large-scale atmospheric fluid dynamics. For stability and efficiency reasons, several of the operational forecasting centres, in particular the Met Office and the European Centre for Medium-Range Weather Forecasts (ECMWF) in the UK, use semi-implicit semi-Lagrangian time-stepping in the dynamical core of the model. The additional burden with this method is that a three-dimensional elliptic partial differential equation (PDE) for the pressure correction has to be solved at every model time step and this often constitutes a significant proportion of the time spent in the dynamical core. In global models, this PDE must be solved in a thin spherical shell. To run within tight operational time-scales, the solver has to be parallelized and there seems to be a (perceived) misconception that elliptic solvers do not scale to large processor counts and hence implicit time-stepping cannot be used in very high-resolution global models. After reviewing several methods for solving the elliptic PDE for the pressure correction and their application in atmospheric models, we demonstrate the performance and very good scalability of Krylov subspace solvers and multigrid algorithms for a representative model equation with more than 1010 unknowns on 65 536 cores on the High-End Computing Terascale Resource (HECToR), the UK's national supercomputer. Here, we tested and optimized solvers from two existing numerical libraries (the Distributed and Unified Numerics Environment (DUNE) and Parallel High Performance Preconditioners (hypre)) and implemented both a conjugate gradient solver and a geometric multigrid algorithm based on a tensor-product approach, which exploits the strong vertical anisotropy of the discretized equation. We study both weak and strong scalability and compare the absolute solution times for all methods; in contrast to one-level methods, the multigrid solver is robust with respect to parameter variations.

58 GEOSCIENCES↗
DOE OSTI2016

Differentiable McCormick relaxations

McCormick's classical relaxation technique constructs closed-form convex and concave relaxations of compositions of simple intrinsic functions. These relaxations have several properties which make them useful for lower bounding problems in global optimization: they can be evaluated automatically, accurately, and computationally inexpensively, and they converge rapidly to the relaxed function as the underlying domain is reduced in size. They may also be adapted to yield relaxations of certain implicit functions and differential equation solutions. However, McCormick's relaxations may be nonsmooth, and this nonsmoothness can create theoretical and computational obstacles when relaxations are to be deployed. This article presents a continuously differentiable variant of McCormick's original relaxations in the multivariate McCormick framework of Tsoukalas and Mitsos. Gradients of the new differentiable relaxations may be computed efficiently using the standard forward or reverse modes of automatic differentiation. Furthermore, extensions to differentiable relaxations of implicit functions and solutions of parametric ordinary differential equations are discussed. A C++ implementation based on the library MC++ is described and applied to a case study in nonsmooth nonconvex optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Subsurface Grain Morphology Reconstruction by Differential Aperture X-ray Microscopy

A multistep, non-destructive grain morphology reconstruction methodology that is applicable to near-surface volumes is developed and tested on synthetic grain structures. This approach probes the subsurface crystal orientation using differential aperture x-ray microscopy on a sparse grid across the microstructure volume of interest. Resulting orientation data are clustered according to proximity in physical and orientation space and used as seed points for an initial Voronoi tessellation to (crudely) approximate the grain morphology. Curvature-driven grain boundary relaxation, simulated by means of the Voronoi implicit interface method, progressively improves the reconstruction accuracy. The similarity between bulk and readily accessible surface reconstruction error provides an objective termination criterion for boundary relaxation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Large-eddy simulation, fuel rod vibration and grid-to-rod fretting in pressurized water reactors

Grid-to-rod fretting (GTRF) in pressurized water reactors is a flow-induced vibration phenomenon that results in wear and fretting of the cladding material on fuel rods. GTRF is responsible for over 70% of the fuel failures in pressurized water reactors in the United States. Predicting the GTRF wear and concomitant interval between failures is important because of the large costs associated with reactor shutdown and replacement of fuel rod assemblies. The GTRF-induced wear process involves turbulent flow, mechanical vibration, tribology, and time-varying irradiated material properties in complex fuel assembly geometries. This paper presents a new approach for predicting GTRF induced fuel rod wear that uses high-resolution implicit large-eddy simulation to drive nonlinear transient dynamics computations. The GTRF fluid–structure problem is separated into the simulation of the turbulent flow field in the complex-geometry fuel-rod bundles using implicit large-eddy simulation, the calculation of statistics of the resulting fluctuating structural forces, and the nonlinear transient dynamics analysis of the fuel rod. Ultimately, the methods developed here, can be used, in conjunction with operational management, to improve reactor core designs in which fuel rod failures are minimized or potentially eliminated. Furthermore, robustness of the behavior of both the structural forces computed from the turbulent flow simulations and the results from the transient dynamics analyses highlight the progress made towards achieving a predictive simulation capability for the GTRF problem.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Accelerating Time Integration for the Shallow Water Equations on the Sphere Using GPUs

The push towards larger and larger computational platforms has made it possible for climate simulations to resolve climate dynamics across multiple spatial and temporal scales. This direction in climate simulation has created a strong need to develop scalable time-stepping methods capable of accelerating throughput on high performance computing. This work details the recent advances in the implementation of implicit time stepping on a spectral element cube-sphere grid using graphical processing units (GPU) based machines. We demonstrate how solvers in the Trilinos project are interfaced with ACME and GPU kernels can significantly increase computational speed of the residual calculations in the implicit time stepping method for the shallow water equations on the sphere. We show the optimization gains and data structure reorganization that facilitates the performance improvements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

This study investigates multiphysics block preconditioners that are critical in devising scalable Newton–Krylov iterative solvers for longer time-scale fully implicit fluid plasma models. The specific model of interest is the visco-resistive, low Mach number, compressible magnetohydrodynamics (MHD) model. This model describes the dynamics of conducting fluids in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics. The specific application of interest that motivates this study is the macroscopic simulation of longer time-scale stability and disruptions of magnetic confinement fusion devices, specifically the ITER Tokamak. The computational solution of the governing balance equations for mass, momentum, heat transfer, and magnetic induction for resistive MHD systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena as well as the significant range of time and length scales that the interactions of these physical mechanisms produce. To handle the range of time and spatial scales of interest, a fully implicit unstructured variational multiscale finite element formulation is employed. For the scalable solution of the Newton linearized systems, fully coupled block preconditioners are designed to leverage algebraic multigrid subsolves. In conclusion, results are presented for the strong and weak scaling of the method as well as the robustness of these techniques for a large range of Lundquist numbers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Newton-Krylov Method in Applications of Solving Two-phase Problems using Drift Flux Model

In this paper, Jacobian-free Newton-Krylov (JFNK) method is investigated in an application to implicitly solve two-phase flow problems using four-equation drift flux model. The closure models include the EPRI drift flux correlations and additional constitutive models to determine flow regimes, wall boiling and interfacial heat/mass transfer, two-phase flow wall friction, etc. Different from many traditional computer codes, fully implicit methods are used for the time integration. The resulted nonlinear discretized equation system is solved using the JFNK method. Expensive and error prone derivation and implementation of the analytical Jacobian matrix are avoided. Numerical results are successfully validated using existing experimental data on flow boiling under forced convection conditions in both pipe and rod bundle geometries.

42 ENGINEERING↗
DOE OSTI2015

Assessing a mini-application as a performance proxy for a finite element method engineering application

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community. However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Evaluation of Density-Functional Tight-Binding Methods for Simulation of Protic Molecular Ion Pairs

In this work, we benchmark the accuracy of the density-functional tight-binding (DFTB) method, namely the long-range corrected second-order (LC-DFTB2) and third-order (DFTB3) models, for predicting energetics of imidazolium-based ionic liquid (IL) ion pairs. We compare the DFTB models against popular density functionals such as LC-ωPBE and B3LYP, using ab initio domain-based local pair-natural orbital coupled cluster (DLPNO-CC) energies as reference. Calculations were carried out in the gas phase, as well as in aqueous solution using implicit solvent methods. We find that the LC-DFTB2 model shows excellent performance in the gas phase and agrees well with reference energies in implicit solvent, often outperforming DFTB3 predictions for complexation energetics. Our study identifies a range of opportunities for use of the LC-DFTB method and quantifies its sensitivity to protonation states and the types of chemical interactions between ion pairs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗