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DOE OSTI2015

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX , is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1999

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗

NASA NTRS2001

Application of Aeroelastic Solvers Based on Navier Stokes Equations

The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors and turbines.

Keith, Theo G., Jr.↗

DOE OSTI2025

Improved internal short circuit models for thermal runaway simulations in lithium-ion batteries

Thermal runaway (TR) modeling is one of the primary tools that can be used to overcome challenges associated with lithium-ion battery (LIB) safety. Among all LIB accidents that have occurred over the past decade, Internal Short Circuit (ISC) remains the most common trigger mechanism. Many available models in the literature either use a simplified approach to simulate ISC or completely ignore its contribution. The aim of this study is to understand the nature of the heat released for different types of ISC scenarios, including aluminum-anode, anode–cathode, and copper-cathode ISC. We study ISC behavior using a coupled electrochemical–thermal model with an integrated TR chemical kinetics solver built in the COMSOL Multiphysics framework. The time duration of heat release and the magnitude of the peak ISC current are studied as functions of parameters such as the size of the penetrating filament and the capacity of the cell. The numerical results are used to build an empirical model validated against the published experimental TR propagation data. Our model can be successfully used as a viable low-cost substitute in lower order (lumped) TR simulations to enable TR prevention and mitigation.

Singh, Bakhshish Preet (ORCID:0000000264751992)↗

DOE OSTI2022

Global gyrokinetic simulations of ASDEX Upgrade up to the transport timescale with GENE–Tango

An accurate description of turbulence up to the transport timescale is essential for predicting core plasma profiles and enabling reliable calculations for designing advanced scenarios and future devices. Here, we exploit the gap separation between turbulence and transport timescales and couple the global gyrokinetic code GENE to the transport-solver Tango, including kinetic electrons, collisions, realistic geometries, toroidal rotation and electromagnetic effects for the first time. This approach overcomes gyrokinetic codes' limitations and enables high-fidelity profile calculations in experimentally relevant plasma conditions, significantly reducing the computational cost. We present numerical results of GENE–Tango for two ASDEX Upgrade discharges, one of which exhibits a pronounced peaking of the ion temperature profile not reproduced by TGLF–ASTRA. We show that GENE–Tango can correctly capture the ion temperature peaking observed in the experiment. By retaining different physical effects in the GENE simulations, e.g., collisions, toroidal rotation and electromagnetic effects, we show that the ion temperature profile's peaking can be linked to electromagnetic effects of submarginal (stable) KBM modes. Furthermore, based on these results, the expected GENE–Tango speedup for the ITER standard scenario is larger than two orders of magnitude compared to a single gyrokinetic simulation up to the transport timescale, possibly making first-principles ITER simulations feasible on current computing resources.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Spectral Equivalence of Low-Order Discretizations for High-Order H(curl) and H(div) Spaces

In this paper, we present spectral equivalence results for high-order tensor product edge- and face-based finite elements for the H(curl) and H(div) function spaces. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the high-order elements are spectrally equivalent to those for an assembly of low-order elements on the associated Gauss--Lobatto--Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscale basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.

58 GEOSCIENCES↗

DOE OSTI2017

A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations

Verification and validation of our solutions for calculating the neutron reactivity for nuclear materials is a key issue to address for many applications, including criticality safety, research reactors, power reactors, and nuclear security. Neutronics codes solve variations of the Boltzmann transport equation. The two main variants are Monte Carlo versus deterministic solutions, e.g. the MCNP [1] versus PARTISN [2] codes, respectively. There have been many studies over the decades that examined the accuracy of such solvers and the general conclusion is that when the problems are well-posed, either solver can produce accurate results. However, the devil is always in the details. The current study examines the issue of self-shielding and the stress it puts on deterministic solvers. Most Monte Carlo neutronics codes use continuous-energy descriptions of the neutron interaction data that are not subject to this effect. The issue of self-shielding occurs because of the discretisation of data used by the deterministic solutions. Multigroup data used in these solvers are the average cross section and scattering parameters over an energy range. Resonances in cross sections can occur that change the likelihood of interaction by one to three orders of magnitude over a small energy range. Self-shielding is the numerical effect that the average cross section in groups with strong resonances can be strongly affected as neutrons within that material are preferentially absorbed or scattered out of the resonance energies. This affects both the average cross section and the scattering matrix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

SNICAR-ADv4: a physically based radiative transfer model to represent the spectral albedo of glacier ice

Abstract. Accurate modeling of cryospheric surface albedo is essential for our understanding of climate change as snow and ice surfaces regulate the global radiative budget and sea-level through their albedo and mass balance. Although significant progress has been made using physical principles to represent the dynamic albedo of snow, models of glacier ice albedo tend to be heavily parameterized and not explicitly connected with physical properties that govern albedo, such as the number and size of air bubbles, specific surface area (SSA), presence of abiotic and biotic light absorbing constituents (LACs), and characteristics of any overlying snow. Here, we introduce SNICAR-ADv4, an extension of the multi-layer two-stream delta-Eddington radiative transfer model with the adding–doubling solver that has been previously applied to represent snow and sea-ice spectral albedo. SNICAR-ADv4 treats spectrally resolved Fresnel reflectance and transmittance between overlying snow and higher-density glacier ice, scattering by air bubbles of varying sizes, and numerous types of LACs. SNICAR-ADv4 simulates a wide range of clean snow and ice broadband albedo (BBA), ranging from 0.88 for (30 µm) fine-grain snow to 0.03 for bare and bubble-free ice under direct light. Our results indicate that representing ice with a density of 650 kg m−3 as snow with no refractive Fresnel layer, as done previously, generally overestimates the BBA by an average of 0.058. However, because most naturally occurring ice surfaces are roughened “white ice”, we recommend modeling a thin snow layer over bare ice simulations. We find optimal agreement with measurements by representing cryospheric media with densities less than 650 kg m−3 as snow and larger-density media as bubbly ice with a Fresnel layer. SNICAR-ADv4 also simulates the non-linear albedo impacts from LACs with changing ice SSA, with peak impact per unit mass of LACs near SSAs of 0.1–0.01 m2 kg−1. For bare, bubble-free ice, LACs actually increase the albedo. SNICAR-ADv4 represents smooth transitions between snow, firn, and ice surfaces and accurately reproduces measured spectral albedos of a variety of glacier surfaces. This work paves the way for adapting SNICAR-ADv4 to be used in land ice model components of Earth system models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1987

Parallel computations and their impact on mechanics; Proceedings of the Symposium, ASME Winter Annual Meeting, Boston, MA, Dec. 13-18, 1987

The conference presents papers on parallel architectures and the programming environment, parallel numerical algorithms, structural mechanics applications, and fluid dynamics applications. Topics include concurrent computer architecture, the state-of-the-art in highly parallel computer systems, supercomputer programming environments, uniquely parallel algorithms, the parallel solution of nonlinear elliptic equations, highly parallel banded systems solvers, and optimal mapping of irregular finite element domains to parallel processors. Consideration is also given to parallel processing in finite element structural analysis, heirarchical parallelism in a finite element CFD algorithm, and a parallelized elliptic solver for reacting flows.

Noor, Ahmed K.↗

NASA NTRS1990

On the prediction of far field computational aeroacoustics of advanced propellers

A numerical method for determining the acoustic far field generated by a high-speed subsonic aircraft propeller was developed. The approach used in this method was to generate the entire three-dimensional pressure field about the propeller (using an Euler flowfield solver) and then to apply a solution of the wave equation on a cylindrical surface enveloping the propeller. The method is applied to generate the three-dimensional flowfield between two blades of an advanced propeller. The results are compared with experimental data obtained in a wind-tunnel test at a Mach number of 0.6.

Jaeger, Stephen M.↗

NASA NTRS2001

Computational Aeroacoustic Analysis System Development

Many industrial and commercial products operate in a dynamic flow environment and the aerodynamically generated noise has become a very important factor in the design of these products. In light of the importance in characterizing this dynamic environment, Rocketdyne has initiated a multiyear effort to develop an advanced general-purpose Computational Aeroacoustic Analysis System (CAAS) to address these issues. This system will provide a high fidelity predictive capability for aeroacoustic design and analysis. The numerical platform is able to provide high temporal and spatial accuracy that is required for aeroacoustic calculations through the development of a high order spectral element numerical algorithm. The analysis system is integrated with well-established CAE tools, such as a graphical user interface (GUI) through PATRAN, to provide cost-effective access to all of the necessary tools. These include preprocessing (geometry import, grid generation and boundary condition specification), code set up (problem specification, user parameter definition, etc.), and postprocessing. The purpose of the present paper is to assess the feasibility of such a system and to demonstrate the efficiency and accuracy of the numerical algorithm through numerical examples. Computations of vortex shedding noise were carried out in the context of a two-dimensional low Mach number turbulent flow past a square cylinder. The computational aeroacoustic approach that is used in CAAS relies on coupling a base flow solver to the acoustic solver throughout a computational cycle. The unsteady fluid motion, which is responsible for both the generation and propagation of acoustic waves, is calculated using a high order flow solver. The results of the flow field are then passed to the acoustic solver through an interpolator to map the field values into the acoustic grid. The acoustic field, which is governed by the linearized Euler equations, is then calculated using the flow results computed from the flow solver.

Hadid, A.↗

DOE OSTI2015

Quantifying Uncertainties through Advanced Theoretical Analysis for Image and Signal Reconstruction NLV-02-15, Year 1 of 2

Presentation describes project to (1) adapt accelerated matrix-free linear system solvers for applying new statistical approaches to very large–scale problems, (2) characterize the degree to which new statistical methods are superior to classical methods in respect to the sensitivity to “tuning parameters,” and (3) develop a new mathematical theory and associated numerical methods for computing the point spread function of an x-ray imaging system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Quantifying Uncertainties Through Advanced Theoretical Analysis for Image and Signal Reconstruction, NLV-02-15, Year 2 of 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

P{sub N} source expansion nodal method in MPACT for boiling water reactors

This paper describes the one-node P{sub N}-Source Expansion Nodal Method (SENM) axial solver for the 2D/1D method recently implemented in MPACT to support Boiling Water Reactors (BWR) analysis. Since the BWR has a more complicated design and strong burnable absorber, the existing PN-Nodal Expansion Method (NEM) axial solver in MPACT may not be sufficient to accurately represent the intranodal flux and source profiles for BWRs. The one-node P{sub N}-SENM has been implemented in this work to reduce the axial spatial discretization error for BWRs. From numerical results, we verify that the P{sub N}-SENM can improve the accuracy of the pin power prediction, and confirm that P{sub N}-SENM can use more than a 1.5 times larger axial mesh size than P{sub N}-NEM to have similar accuracy for the BWR GE14 3D assembly problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Numerical discreteness errors in multispecies cosmological N -body simulations

ABSTRACT We present a detailed analysis of numerical discreteness errors in two-species, gravity-only, cosmological simulations using the density power spectrum as a diagnostic probe. In a simple set-up where both species are initialized with the same total matter transfer function, biased growth of power forms on small scales when the solver force resolution is finer than the mean interparticle separation. The artificial bias is more severe when individual density and velocity transfer functions are applied. In particular, significant large-scale offsets in power are measured between simulations with conventional offset grid initial conditions when compared against converged high-resolution results where the force resolution scale is matched to the interparticle separation. These offsets persist even when the cosmology is chosen so that the two particle species have the same mass, indicating that the error is sourced from discreteness in the total matter field as opposed to unequal particle mass. We further investigate two mitigation strategies to address discreteness errors: the frozen potential method and softened interspecies short-range forces. The former evolves particles under the approximately ‘frozen’ total matter potential in linear theory at early times, while the latter filters cross-species gravitational interactions on small scales in low-density regions. By modelling closer to the continuum limit, both mitigation strategies demonstrate considerable reductions in large-scale power spectrum offsets.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2013

Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This proposal describes an approach to validate the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft. The research described here is absolutely cutting edge. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional"validation by test only'' mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computationaf Fluid Dynamics can be used to veritY these requirements; however, the model must be validated by test data. The proposed research project includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT and OPEN FOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid . . . Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. To date, the author is the only person to look at the uncertainty in the entire computational domain. For the flow regime being analyzed (turbulent, threedimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Groves, Curtis E.↗

NASA NTRS2014

Dissertation Defense: Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Fluid Dynamics↗