Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “spectral element method”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the largeamplitude collective motion of quantum many-body systems such as atomic nuclei. Under the GaussianOverlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in amulti-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solvesthe collective Schrödinger equation in a finite element basis. This new version features: (i) the ability tosolve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) supportfor new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonianand overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylovapproximation of the time propagator for time integration instead of the implicit Crank–Nicolson methodimplemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on ananalytic problem as well as on realistic two-dimensional calculations of the low-energy fission of240Puand256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplexelements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectralelement method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fissionmass distributions of240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numericalprecision of a few percents).

Regnier, D.↗
NASA NTRS1987

A well-posed optimal spectral element approximation for the Stokes problem

A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.

Maday, Y.↗
DOE OSTI2025

High-Fidelity CFD Simulation of Mixed Convection and Forced Convection in a Pebble Bed Test Reactor Core

The Hermes low-power [35-MW(thermal)] reactor will be built and operated by Kairos Power LLC (KP) to demonstrate its fluoride salt-cooled high-temperature reactor (FHR) technology. In the KP FHR, the reactor core is composed of randomly packed pebbles with TRISO fuel particles inside with FLiBe flow upward through the core acting as a coolant. Previous numerical and experimental studies have been limited to either a small-size bed or to a lack of detailed measurements for heat transfer. Here, to address the lack of high-fidelity heat transfer data in a real-size FHR core, in this study, we simulated a pebble bed core with 34 374 pebbles randomly packed, similar to the Hermes reactor's size. The core radius was 14 times that of the pebble diameter, while the core height was 45 times. In this work, we were particularly interested in a mixed convection regime, where buoyancy is important. Therefore, we performed several large-eddy simulations at different Reynolds numbers (160 to 1000) with gravitational force included. The spectral element computational fluid dynamics code NekRS with graphics processing unit acceleration was used for this study. The low-Mach number approximation was applied to address property changes in the FLiBe and to account for buoyancy. A pure hexahedral mesh with 60 million elements was generated by the Voronoi cell method. At the polynomial order of 5, the total degrees of freedom was 7.5 billion. The developed case in this work is the first of its kind in terms of size and complexity. The local numerical data across the domain were obtained and compared with empirical correlations. After examining the data, we found the following conclusions. For pressure drop, the Reger correlation predicted less than a 5% error. On the other hand, for heat transfer, the Wakao correlation outperformed the others. Based on our findings, we recommend the use of the Wakao correlation for the Nusselt number calculation, and for pressure drop, the KTA (Kerntechnischer Ausschuss) correclation, among the available experimental correlations. In conclusion, the Reger direct numerical simulation-driven correlation for pressure drops should also be considered, given its best agreement with our calculations.

Mixed Convection↗
DOE OSTI2019

Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard DG method. Numerical results are shown demonstrating the effectiveness of the method on a variety of test cases, including Burgers’ equation and the Euler equations, in one, two, and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Modeling curved interfaces without element‐partitioning in the extended finite element method

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

Chin, Eric B.↗
DOE OSTI2022

Investigation of Cycle-to-Cycle Variations in Internal Combustion Engine Using Proper Orthogonal Decomposition

The understanding, modeling and control of the cycle-to-cycle variation (CCV) in the modern internal combustion engine (ICE) is a key scientific challenge to achieve stable engine operation. High CCV in the engine combustion chamber may contribute to partial burn, misfire and knock, which adversely affects the engine performance and may potentially damage the engine. The objective of the current study is to leverage high-fidelity numerical simulations to improve the understanding of the causes of CCV. Using the massively parallel code, Nek5000, multi-cycle, wall-resolved large-eddy simulations (LES) were performed for the General Motors (GM), Transparent Combustion Chamber (TCC-III) optical engine under motored operating conditions. Further, the large-scale structures of the in-cylinder flow were investigated using a triple proper orthogonal decomposition (POD) technique to explore the characteristics of different parts of the flow and their contributions to CCV. The kinetic energy of the subset of flow structures were determined and correlated between the intake and compression strokes. The insights from the analysis of the large-scale flow structures will be used to assist the development of improved engine designs with reduced CCV and enhance the engine performance.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Investigating the Origins of Cyclic Variability in Internal Combustion Engines Using Wall-Resolved Large Eddy Simulations

Modern internal combustion engines (ICE) operate at the ragged edge of stable operation characterized by high cycle-to-cycle variations (CCV). A key scientific challenge for ICE is the understanding, modeling, and control of CCV in engine performance, which can contribute to partial burns, misfire, and knock. The objective of this study is to use high-fidelity numerical simulations to improve the understanding of the causes of CCV. Nek5000, a leading high-order spectral element, open source code, is used to simulate the turbulent flow in the engine combustion chamber. Multicycle, wall-resolved large-eddy simulations (LESs) are performed for the General Motors (GM), Transparent Combustion Chamber (TCC-III) optical engine under motored operating conditions. The mean and root-mean-square (rms) of the in-cylinder flow fields at various piston positions are validated using particle image velocimetry (PIV) measurements during the intake and compression strokes. The large-scale flow structures, including the swirl and tumble flow patterns, are analyzed in detail and the causes for cyclic variabilities in these flow features are explained. The energy distribution across the different scales of the flow are quantified using one-dimensional (1D) energy spectra, and the effect of the tumble breakdown process on the energy distribution is examined. Finally, the insights from this study can help us develop improved engine designs with reduced cyclic variabilities in the in-cylinder flow leading to enhanced engine performance.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2017

Exascale Programming Approaches for Accelerated Climate Modeling for Energy

The Accelerated Climate Modeling for Energy (ACME) program is a leading-edge climate and Earth system model designed to address the U.S. Department of Energy (DOE) mission needs. The ACME project involves collaboration between seven National Laboratories, the National Center for Atmospheric Research, four academic institutions, and one private-sector company. The ACME project funds ongoing efforts to ensure the model continues to make efficient use of DOE Leadership Computing Facilities (LCFs) in order to best address the three driving grand challenge science questions:Water cycle: How will more realistic portrayals of features important to the water cycle (resolution, clouds, aerosols, snowpack, river routing, land use) affect river flow and associated freshwater supplies at the watershed scale?Cryosphere systems: Could a dynamical instability in the Antarctic ice sheet be triggered within the next 40 years?Biogeochemistry: What are the contributions and feedbacks from natural and managed systems to current greenhouse gas fluxes, and how will those factors and associated fluxes evolve in the future?

Norman, Matthew↗
DOE OSTI2019

InSight, 3D modeling CTX impact [Slides]

This technical report contains a set of slides intended for the Insight Impact Working Group. It discusses how the project is working on benchmarking between SPECFEM3D and AXISEM, how a hypothesis is needed in relation to the data on the thickness of the regolith layer, and the need to develop a 3D model of scattering.

58 GEOSCIENCES↗
DOE OSTI2021

2021 Summer SPE Project

SPE is a project in order to develop new, more physics-based, seismic models of explosions (see Nelson et al. 2013). One key component of this effort is numerical modeling enabled by modern state-of-art code/software. Accurate modeling of the shape and amplitude of seismic waves from their generation to their propagation to remote monitoring seismic stations is important to our ability to determine the origin and strength of the source from remote recording. In this project, the modeling is performed by coupling two codes HOSS and SPECFEM3D. HOSS models the dynamic nonlinear processes happening near the explosion. SPECFEM3D computes the propagation of seismic waves as they travel through 3D complex Earth models. SPECFEM3D was modified in order to be driven by a set of time-series calculated by HOSS in lieu of a seismic source. The goal of this summer project is the investigation of several questions pertinent to the establishment of a full end-to-end modeling capability from the high-rate strain regime area to remote distances where seismic station record seismic waves generated by explosions. The investigated questions are: (1) How to perform proper filtering? Direct-solution modeling only sustains a limited range of frequency depending on the grid size. As we go from one modeling domain to the other via coupling, the mesh size is getting coarser to allow modeling at large scale but also to account for the fact that high-frequency waves do not physically travel to large distances. So filtering of the time-series generated by the near-field hydrodynamic modeling is a current practice often employed but its effects on the modeled waveforms has to be investigated. (2) Quantitative assessment of the efficiency of attenuation to remove high-frequency content of the wavefield. This assessment will allow to create meshes with a grid size appropriate to the actual physics of wave propagation for a given explosion. (3) Checking that the coupling process and the two codes respect the cylindrical symmetry that is expected in the case of a pure explosion in a half-space. (4) The effect of the state-of-stress in the near-source area on the modeled seismic waveforms. These questions will be investigated through the modeling of SPE-4P, the fourth explosion of this series because it was designed to have little interaction with the geologic surrounding and the free surface of the Earth so that it is the most explosion-like experiment, with the most symmetries to be verified.

58 GEOSCIENCES↗
DOE OSTI2021

Scalable Interpolation on GPUs for Thermal Fluids Applications

The need for efficient interpolation arises in many use cases for spectral element simulations. Towards this end, we present a fast and robust GPU-enable interpolation utility for NekRS, a spectral-element, Navier-Stokes solver. This utility is based on the findpts and findpts eval routines from the gslib library. To demonstrate the functionality, we added support for particle tracking. The GPU implementation of the interpolation allows for tracking 100 times more particles for the same computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

High-Order Hybrid RANS-LES Study of NACA0012 Wing Sections

We develop hybrid RANS-LES strategies within Nek5000 for application to airfoil sections at small flight configurations. We present a validation and verification study of $k \space – \space \tau$ SST applied to a NACA 0012 wing section in a pure RANS and in a hybrid RANS-LES setup. The study shows good corroboration with existing experimental and numerical datasets. We also analyze some of the observed discrepancies with the experiments by evaluating the side wall “blocking” effect. We demonstrate that for the hybrid turbulence modeling approach a high-order spectral- element discretization converges faster (i.e., with less resolution) than a representative low-order finite-volume-based approach.

42 ENGINEERING↗
NASA NTRS1989

Numerical algorithms for computations of feedback laws arising in control of flexible systems

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Lasiecka, Irena↗
DOE OSTI2017

Formulation and Validation of an Efficient Computational Model for a Dilute, Settling Suspension Undergoing Rotational Mixing

Designing processing equipment for the mixing of settling suspensions is a challenging problem. Achieving low-cost mixing is especially difficult for the application of slowly reacting suspended solids because the cost of impeller power consumption becomes quite high due to the long reaction times (batch mode) or due to large-volume reactors (continuous mode). Further, the usual scale-up metrics for mixing, e.g., constant tip speed and constant power per volume, do not apply well for mixing of suspensions. As an alternative, computational fluid dynamics (CFD) can be useful for analyzing mixing at multiple scales and determining appropriate mixer designs and operating parameters. We developed a mixture model to describe the hydrodynamics of a settling cellulose suspension. The suspension motion is represented as a single velocity field in a computationally efficient Eulerian framework. The solids are represented by a scalar volume-fraction field that undergoes transport due to particle diffusion, settling, fluid advection, and shear stress. A settling model and a viscosity model, both functions of volume fraction, were selected to fit experimental settling and viscosity data, respectively. Simulations were performed with the open-source Nek5000 CFD program, which is based on the high-order spectral-finite-element method. Simulations were performed for the cellulose suspension undergoing mixing in a laboratory-scale vane mixer. The settled-bed heights predicted by the simulations were in semi-quantitative agreement with experimental observations. Further, the simulation results were in quantitative agreement with experimentally obtained torque and mixing-rate data, including a characteristic torque bifurcation. In future work, we plan to couple this CFD model with a reaction-kinetics model for the enzymatic digestion of cellulose, allowing us to predict enzymatic digestion performance for various mixing intensities and novel reactor designs.

09 BIOMASS FUELS↗
NASA NTRS2002

Aircraft Engine Noise Scattering - A Discontinuous Spectral Element Approach

The paper presents a time-domain method for computation of sound radiation from aircraft engine sources to the far-field. The effects of nonuniform flow around the aircraft and scattering of sound by fuselage and wings are accounted for in the formulation. Our approach is based on the discretization of the inviscid flow equations through a collocation form of the Discontinuous Galerkin spectral element method. An isoparametric representation of the underlying geometry is used in order to take full advantage of the spectral accuracy of the method. Largescale computations are made possible by a parallel implementation based on message passing. Results obtained for radiation from an axisymmetric nacelle alone are compared with those obtained when the same nacelle is installed in a generic con.guration, with and without a wing.

Stanescu, D.↗
NASA NTRS2000

Real-time simulation of dynamically deformable finite element models using modal analysis and spectral Lanczos decomposition methods

We present two efficient methods for simulating real-time behavior of a dynamically deformable 3D object modeled by finite element equations. The first method is based on modal analysis, which uses the most significant vibration modes of the object to compute the deformations in real-time for applied forces. The second method uses the spectral Lanczos decomposition to obtain the explicit solutions of the finite element equations.

medical↗