Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical algorithms”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A finite element formulation for deformation twinning induced strain localization in polycrystal magnesium alloys

Deformation twinning induces shear strain localization in hexagonal close-packed crystals and is critical for the material’s ductility and failure. Cracks often occur at twin-twin or twin-grain boundary intersections and propagate along twin bands. However, most crystal plasticity models for deformation twinning are based on a “pseudo-slip” approach and do not capture the localized deformation associated with the formation of each discrete twin band. The few exceptions are discrete twin models that involve very complex numerical algorithms and are often compromised in accuracy due to the numerical convergence. These factors make the discrete twin models hard to adopt. This paper proposes a modification to the conventional finite element weak form, to fully incorporate a twin-induced heterogeneous deformation that does not depend on the “pseudo-slip” assumption. The model starts by splitting the deformation gradient into elastic-slip-twinning components. The twin-induced deformation gradient component is computed separately by solving a microstructural evolution problem and then implemented into finite element weak form by constructing a global “twin-force” vector. The constitutive update (e.g., in the user-defined material subroutine, or UMAT, for ABAQUS) therefore avoids dealing with the twinning and recovers to the form of a regular slip-based crystal plasticity model. The results presented here indicate that the twin-induced strain localization and the associated stress-reversal phenomena near the twin band were naturally captured in the model, which was validated against an in-situ synchrotron X-ray micro-diffraction experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

42 ENGINEERING↗
DOE OSTI2020

Coupled Electro-Thermal Analysis of Permanent Magnet Synchronous Motor for Electric Vehicles

Permanent magnet synchronous motors (PMSM) are extensively used in electric vehicles. However, high internal heat generation and inefficient heat dissipation often limit the operational reliability, and longevity of the PMSM. Therefore, proper quantification of heat generation in electric motor and advanced embedded motor cooling techniques remain topics of immense interest. In order to accurately predict electro-magnetic performance, i.e., efficiency, component-wise heat losses and the corresponding temperature distribution of a jacket cooled machine, this paper presents a two-way iteratively coupled electro-thermal modeling framework. Finite element based software Motor-CAD has been utilized for electro-magnetic performance calculation of BMW i3 PMSM. Finite volume based computational fluid dynamics/heat transfer (CFD/HT) software ANSYS® FLUENT® has been employed to simulate the temperature distribution of the PMSM, using the electro-magnetic losses as heat input. Computed heat losses, stator, winding, rotor, and magnet temperatures are utilized as coupling parameters between the electro-magnetic and thermal models. A conventional one-way coupling algorithm has also been developed and compared to the newly proposed two-way coupling algorithm. Numerical results confirm that at high current density, one-way coupling algorithm significantly over-predicts the motor temperature compared to the two-way algorithm. A comprehensive analysis has been carried out to characterize the influences of current density, speed, and forced convection heat transfer coefficient on the heat losses, overall efficiency, and maximum temperature of the PMSM. Lastly, an efficiency map has been interpreted from the coupled electro-magnetic simulation.

42 ENGINEERING↗
DOE OSTI2020

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. In this report we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

42 ENGINEERING↗
DOE OSTI2021

Thermodynamically consistent algorithms for models of incompressible multiphase polymer solutions with a variable mobility

Here we present a general strategy for developing structure and property preserving numerical algorithms for thermodynamically consistent models of incompressible multiphase polymer solutions with a variable mobility. We first present a formalism to derive thermodynamically consistent, incompressible, multiphase polymer models. Then, we develop the general strategy, known as the supplementary variable method, to devise thermodynamically consistent numerical approximations to the models. We illustrate the numerical strategy using newly developed models of incompressible diblock copolymer solutions coupled with an electric and a magnetic field, respectively. Mesh refinement is conducted to verify convergence rates of the developed schemes. Some numerical examples are given to exhibit underlying dynamics absent from and driven by the external fields, respectively, highlighting differences between models with the variable and constant mobilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Estimation of the Water Table Position in Unconfined Aquifers with MODFLOW 6

Abstract The numerical estimation of the position of the water table in unconfined aquifers is important for many practical applications. Its determination through observations or analytical methods is restricted to a few cases. Therefore, it is often estimated through numerical simulations, which may be affected by numerical artifacts and/or poor stability. We use MODFLOW to estimate the position of the water table for a seemingly simple example problem and demonstrate difficulties that can be faced when performing this kind of numerical simulation. We explain the causes for the numerical challenges that originate from the properties of the mathematical equations that must be solved. Based on the results of more than 600 steady‐state simulations, we show how the stability of the numerical solution can be affected by the values of physical parameters that define the problem (e.g., recharge rate, anisotropy ratio, and other parameters that control the numerical algorithm such as settings of the linear and nonlinear solution methods). Finally, we comment on some best practices to apply numerical simulations to estimate the water table position.

Geology↗
DOE OSTI2024

Development of High-Fidelity and Efficient Modeling Capabilities for Enabling Co-Optimization of Fuels and Multi-Mode Engines

The objective of this closely coordinated research project is to develop improved physical sub-models and innovative numerical algorithms to enable accurate and efficient predictions of multi-mode combustion to support EERE’s Co-Optima program. To this end, a research pro-gram is proposed that seeks • to develop accurate submodels for predicting multi-mode combustion regimes, wall-heat transfer, non-equilibrium plasma ignition, and combustion-mode transition, • to develop dynamic load-rebalancing algorithms and efficient semi-implicit time-integration schemes for enabling exascale computing, • to validate the computational submodels against experiments and direct numerical simulation (DNS) data in conjunction with sensitivity analysis, and • to support the direct transition of the resulting sub-models into other engine-simulation tools through the development of self-contained modules. All sub-models will be integrated into the open-source exascale engine-simulation platform Nek5000.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Asynchronous Iterative Solvers for Extreme-Scale Computing

The Asynchronous Iterative Solvers for Extreme-Scale Computing (AsyncIS) project aims to explore more efficient numerical algorithms by decreasing their overhead. AsyncIS does this by replacing the outer Krylov subspace solver with an asynchronous optimized Schwarz method, thereby removing the global synchronization and bulk synchronous operations typically used in numerical codes. AsyncIS—a U.S. Department of Energy (DOE)-funded collaboration between Georgia Tech, the University of Tennessee, Knoxville, Temple University, and Sandia National Laboratories—also focuses on the development and optimization of asynchronous preconditioners (i.e., preconditioners that are generated and/or applied in an asynchronous fashion). The novel preconditioning algorithms that provide fine-grained parallelism enable preconditioned Krylov solvers to run efficiently on large-scale distributed systems and manycore accelerators like GPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

pyDRESCALk

Modern data scientists are tasked to analyze ever-growing data sets with increasingly complex relationships. Tensor decompositions have come to play a central role in identifying underlying latent structures in higher-order data. The problem of fitting tensor models to different distributions is complicated by the combinations of size, dimensionality, and sparsity present in real world data. The situation demands efficient algorithms designed for shared-memory and distributed systems. This work will present new research that tackles these challenges on several different fronts, leveraging optimizations in numerical algorithms and sparse tensor representations in heterogeneous high performance computing environments.

Bhattarai, Manish↗
DOE OSTI2023

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations—usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. Furthermore, the resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A beginner's guide to non-abelian iPEPS for correlated fermions

Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension D=24 D = 24 on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with 2 2 bands of spinful fermions of \mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb} S U ( 2 ) s p i n ⊗ S U ( 2 ) o r b symmetry, the other with 3 3 flavors of spinless fermions of \mathrm{SU}(3)_\mathrm{flavor} S U ( 3 ) f l a v o r symmetry.

Bruognolo, Benedikt↗
DOE OSTI2024

GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. Here, this has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Causal explicit algorithm for heat conduction in a plasma

Hyperbolic heat conduction extends standard Spitzer-Harm heat conduction by including a term proportional to the time derivative of the heat flux. The new term arises from a kinetic derivation of the heat flux that includes higher order corrections. Here we present a causal explicit numerical algorithm for solving the nonlinear hyperbolic heat conduction equation in an unmagnetized plasma. The maximum stable timestep for the causal explicit algorithm scales linearly with the cell size, owing to the hyperbolic nature of the problem. This is in contrast to the quadratic scaling of the maximum stable timestep with the cell size for the parabolic forward time centered space algorithm. The favorable scaling of the timestep with the cell size enables a practical explicit implementation of heat conduction in high-performance massively parallel plasma codes. In particular, we have implemented the causal explicit algorithm in the laser plasma interaction code pF3D. We verify the CE algorithm and analyze its convergence rate by simulating a harmonic mode, which has an analytic solution within the context of the HHC model. We also compare simulations using the CE algorithm to those using the forward time centered space algorithm on a pair of test problems: evolution in time of a Gaussian temperature perturbation in a uniform plasma and heat transport in the presence of inverse bremsstrahlung heating by a Gaussian laser speckle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Neural Networks-Based Inverter Control: Modeling and Adaptive Optimization for Smart Distribution Networks

The optimal voltage control of inverter-based resources, especially under the high penetration of solar photovoltaics, is critical to the stability of the distribution power system. However, the computational complexity as well as the coordinated operation performance of the voltage control optimization in the distribution power system limits the real-time applications. To mitigate this issue, a model-free based adaptive optimal control scheme for the smart inverter is proposed to maximize the active power generation, minimize the power loss, and maintain the bus voltages in smart distribution networks. An inverter-based optimization model for coordinated operation is first established, considering the uncertainties of renewable power generation. Subsequently, by collecting the data and control strategies, the neural networks (NNs) based algorithm is proposed to efficiently predict the best possible control strategy. The main objective of this scheme is to accurately predict candidate optimal solutions with near-negligible feasibility and optimization gaps, with the advantage of avoiding complicated iteration-based numerical algorithms. Thereafter, the co-simulation among OpenDSS, MATLAB, and Python is set up to fully take advantage of the three individual software. Experiments are conducted based on different control parameter characteristics and structures of NNs. Finally, the results reveal that an average mean squared error of 0.013 and 1 ms response time are achieved, which is lower than some state-of-the-art methods.

42 ENGINEERING↗
DOE OSTI2025

Euler equations and the Sod shock tube problem

The Euler equations are a subset of the magnetohydrodynamic (MHD) equations in the infinitely collisional, unmagnetized limit. MHD modeling is central to many areas of plasma physics, ranging from low-temperature glow discharges to inertial confinement fusion. An important aspect of the Euler equations is their ability to describe states with discontinuities, such as shock waves. A standard benchmark test for numerical implementation of the Euler equations is the Sod shock tube. In this test, the system is initialized at rest with a pressure and density discontinuity, which results in a shock wave traveling into the low-pressure region and a rarefaction wave traveling into the high-pressure region. Starting with the presentation of the Euler equations, a numerical algorithm is presented here to solve these equations in one dimension. This is followed by an overview of the Sod shock tube problem that includes the precise initial setup and the analytic solution. Finally, the analytic solution is compared with results from numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗
DOE OSTI2020

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗