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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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At least 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Reduced-order modeling for nonlocal diffusion problems

In several settings, diffusive behavior is observed to not follow the rate of spread predicted by parabolic partial differential equations (PDEs) such as the heat equation. Such behaviors, often referred to as anomalous diffusion, can be modeled using nonlocal equations for which points at a finite distance apart can interact. An example of such models is provided by fractional derivative equations. Because of the nonlocal interactions, discretized nonlocal systems have less sparsity, often significantly less, compared with corresponding discretized PDE systems. As such, the need for reduced-order surrogates that can be used to cheaply determine approximate solutions is much more acute for nonlocal models compared with that for PDEs. In this paper, we consider the construction, application, and testing of proper orthogonal decomposition (POD) reduced models for an integral equation model for nonlocal diffusion. For certain modeling parameters, the model we consider allows for discontinuous solutions and includes fractional Laplacian kernels as a special case. Preliminary computational results illustrate the potential of using POD to obtain accurate approximations of solutions of nonlocal diffusion equations at much lower costs compared with, for example, standard finite element methods. Copyright © 2016 John Wiley & Sons, Ltd.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Institute for High Heat Flux Removal (IHHFR). Phases I, II, and III

The IHHFR focused on interdisciplinary applications as it relates to high heat flux engineering issues and problems which arise due to engineering systems being miniaturized, optimized, or requiring increased high heat flux performance. The work in the IHHFR focused on water as a coolant and includes: (1) the development, design, and construction of the high heat flux flow loop and facility; (2) test section development, design, and fabrication; and, (3) single-side heat flux experiments to produce 2-D boiling curves and 3-D conjugate heat transfer measurements for single-side heated test sections. This work provides data for comparisons with previously developed and new single-side heated correlations and approaches that address the single-side heated effect on heat transfer. In addition, this work includes the addition of single-side heated circular TS and a monoblock test section with a helical wire insert. Finally, the present work includes: (1) data base expansion for the monoblock with a helical wire insert (only for the latter geometry), (2) prediction and verification using finite element, (3) monoblock model and methodology development analyses, and (4) an alternate model development for a hypervapotron and related conjugate heat transfer controlling parameters.

2-D Boiling Curves↗
DOE OSTI2016

Fast computation of synthetic seismograms within a medium containing remote localized perturbations: a numerical solution to the scattering problem

We derive a fast discrete solution to the scattering problem. This solution allows us to compute accurate synthetic seismograms or waveforms for arbitrary locations of sources and receivers within a medium containing localized perturbations. The key to efficiency is that wave propagation modelling does not need to be carried out in the entire volume that encompasses the sources and the receivers but only within the subvolume containing the perturbations or scatterers. The proposed solution has important applications, for example, it permits the imaging of remote targets located in regions where no sources or receivers are present. Our solution relies on domain decomposition: within a small volume that contains the scatterers, wave propagation is modelled numerically, while in the surrounding volume, where the medium isn't perturbed, the response is obtained through wavefield extrapolation. The originality of this work is the derivation of discrete formulas for representation theorems and Kirchhof–Helmholtz integrals that naturally adapt to the numerical scheme employed for modelling wave propagation. Our solution applies, for example, to finite difference methods or finite/spectral elements methods. The synthetic seismograms obtained with our solution can be considered ‘exact’ as the total numerical error is comparable to that of the method employed for modelling wave propagation. We detail a basic implementation of our solution in the acoustic case using the finite difference method and present numerical examples that demonstrate the accuracy of the method. We show that ignoring some terms accounting for higher order scattering effects in our solution has a limited effect on the computed seismograms and significantly reduces the computational effort. Finally, we show that our solution can be used to compute localized sensitivity kernels and we discuss applications to target oriented imaging. Extension to the elastic case is straightforward and summarized in a dedicated section.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An efficient parallel simulation of unsteady blood flows in patient-specific pulmonary artery

Simulation of blood flows in the pulmonary artery provides some insight into certain diseases by examining the relationship between some continuum metrics, eg, the wall shear stress acting on the vascular endothelium, which responds to flow-induced mechanical forces by releasing vasodilators/constrictors. V. Kheyfets, in his previous work, studies numerically a patient-specific pulmonary circulation to show that decreasing wall shear stress is correlated with increasing pulmonary vascular impedance. We develop a scalable parallel algorithm based on domain decomposition methods to investigate an unsteady model with patient-specific pulsatile waveforms as the inlet boundary condition. The unsteady model offers tremendously more information about the dynamic behavior of the flow field, but computationally speaking, the simulation is a lot more expensive since a problem which is similar to the steady-state problem has to be solved many times, and therefore, the traditional sequential approach is not suitable anymore. We show computationally that simulations using the proposed parallel approach with up to 10 000 processor cores can be obtained with much reduced compute time. Finally, this makes the technology potentially usable for the routine study of the dynamic behavior of blood flows in the pulmonary artery, in particular, the changes of the blood flows and the wall shear stress in the spatial and temporal dimensions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Seismic waves in medium with poroelastic/elastic interfaces: a two-dimensional P-SV finite-difference modelling

SUMMARY We present a new methodology of the finite-difference (FD) modelling of seismic wave propagation in a strongly heterogeneous medium composed of poroelastic (P) and (strictly) elastic (E) parts. The medium can include P/P, P/E and E/E material interfaces of arbitrary shapes. The poroelastic part can be with (i) zero resistive friction, (ii) non-zero constant resistive friction or (iii) JKD model of the frequency-dependent permeability and resistive friction. Our FD scheme is capable of subcell resolution: a material interface can have an arbitrary position in the spatial grid. The scheme keeps computational efficiency of the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces). Numerical tests against independent analytical, semi-analytical and spectral-element methods prove the efficiency and accuracy of our FD modelling. In numerical examples, we indicate effect of the P/E interfaces for the poroelastic medium with a constant resistive friction and medium with the JKD model of the frequency-dependent permeability and resistive friction. We address the 2-D P-SV problem. The approach can be readily extended to the 3-D problem.

58 GEOSCIENCES↗
DOE OSTI2020

Improving climate model coupling through a complete mesh representation: a case study with E3SM (v1) and MOAB (v5.x)

One of the fundamental factors contributing to the spatiotemporal inaccuracy in climate modeling is the mapping of solution field data between different discretizations and numerical grids used in the coupled component models. The typical climate computational workflow involves evaluation and serialization of the remapping weights during the preprocessing step, which is then consumed by the coupled driver infrastructure during simulation to compute field projections. Tools like Earth System Modeling Framework (ESMF) and TempestRemap offer capability to generate conservative remapping weights, while the Model Coupling Toolkit (MCT) that is utilized in many production climate models exposes functionality to make use of the operators to solve the coupled problem. However, such multistep processes present several hurdles in terms of the scientific workflow and impede research productivity. In order to overcome these limitations, we present a fully integrated infrastructure based on the Mesh Oriented datABase (MOAB) library, which allows for a complete description of the numerical grids and solution data used in each submodel. Through a scalable advancing-front intersection algorithm, the supermesh of the source and target grids are computed, which is then used to assemble the high-order, conservative, and monotonicity-preserving remapping weights between discretization specifications. The Fortran-compatible interfaces in MOAB are utilized to directly link the submodels in the Energy Exascale Earth System Model (E3SM) to enable online remapping strategies in order to simplify the coupled workflow process. We demonstrate the superior computational efficiency of the remapping algorithms in comparison with other state-of-the-science tools and present strong scaling results on large-scale machines for computing remapping weights between the spectral element atmosphere and finite volume discretizations on the polygonal ocean grids.

58 GEOSCIENCES↗
DOE OSTI2016

An n -material thresholding method for improving integerness of solutions in topology optimization

It is common in solving topology optimization problems to replace an integer-valued characteristic function design field with the material volume fraction field, a real-valued approximation of the design field that permits "fictitious" mixtures of materials during intermediate iterations in the optimization process. This is reasonable so long as one can interpolate properties for such materials and so long as the final design is integer valued. For this purpose, we present a method for smoothly thresholding the volume fractions of an arbitrary number of material phases which specify the design. This method is trivial for two-material design problems, for example, the canonical topology design problem of specifying the presence or absence of a single material within a domain, but it becomes more complex when three or more materials are used, as often occurs in material design problems. We take advantage of the similarity in properties between the volume fractions and the barycentric coordinates on a simplex to derive a thresholding, method which is applicable to an arbitrary number of materials. As we show in a sensitivity analysis, this method has smooth derivatives, allowing it to be used in gradient-based optimization algorithms. Finally, we present results, which show synergistic effects when used with Solid Isotropic Material with Penalty and Rational Approximation of Material Properties material interpolation functions, popular methods of ensuring integerness of solutions.

42 ENGINEERING↗
DOE OSTI2013

A Local Incident Flux Response Expansion Transport Method for Coupling to the Diffusion Method in Cylindrical Geometry

A local incident flux response expansion transport method is developed to generate transport solutions for coupling to diffusion theory codes regardless of their solution method (e.g., fine mesh, nodal, response based, finite element, etc.) for reactor core calculations in both two-dimensional (2-D) and three-dimensional (3-D) cylindrical geometries. In this approach, a Monte Carlo method is first used to precompute the local transport solution (i.e., response function library) for each unique transport coarse node, in which diffusion theory is not valid due to strong transport effects. The response function library is then used to iteratively determine the albedo coefficients on the diffusion-transport interfaces, which are then used as the coupling parameters within the diffusion code. This interface coupling technique allows a seamless integration of the transport and diffusion methods. The new method retains the detailed heterogeneity of the transport nodes and naturally constructs any local solution within them by a simple superposition of local responses to all incoming fluxes from the contiguous coarse nodes. A new technique is also developed for coupling to fine-mesh diffusion methods/codes. The local transport method/module is tested in 2-D and 3-D pebble-bed reactor benchmark problems consisting of an inner reflector, an annular fuel region, and a controlled outer reflector. It is found that the results predicted by the transport module agree very well with the reference fluxes calculated directly by MCNP in both benchmark problems.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Parallel Element-based Algebraic Multigrid for H (c url ) and H (div) Problems Using the ParELAG Library

This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H (c url ) and H (div) formulations. ParELAG constructs hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries

Here, we propose a method that morphs high-order meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero isocontour of a smooth discrete function. Common examples of this scenario include using level set functions to represent material interfaces in multimaterial configurations, and evolving geometries in shape and topology optimization. The proposed method formulates the mesh optimization problem as a variational minimization of the sum of a chosen mesh-quality metric using the Target-Matrix Optimization Paradigm (TMOP) and a penalty term that weakly forces the selected faces of the mesh to align with the target surface. The distinct features of the method are use of a source mesh to represent the level set function with sufficient accuracy, and adaptive strategies for setting the penalization weight and selecting the faces of the mesh to be fit to the target isocontour of the level set field. We demonstrate that the proposed method is robust for generating boundary- and interface-fitted meshes for curvilinear domains using different element types in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Eigenvalue Solver for Fluid and Kinetic Plasma Models in Arbitrary Magnetic Topology

ArbiTER (Arbitrary Topology Equation Reader) is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models. The primary application area envisioned is boundary plasma physics in magnetic confinement devices; however ArbiTER should be applicable to other science and engineering fields as well. The code permits a variable numbers of dimensions, making possible application to both fluid and kinetic models. Additionally, the use of specialized equation and topology parsers permits a high degree of flexibility in specifying the physics and geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release

This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole-1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

On ParELAG's Parallel Element-based Algebraic Multigrid and its MFEM Miniapps for H(curl) and H(div) Problems: a report including lowest and next to the lowest order numerical results

This paper presents the utilization of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H(curl) and H(div) formulations. This involves the construction of hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On computing the evolution of temperature for materials under dynamic loading

Modeling and simulation of the dynamic response of materials is important to many applications including the development of armor systems, understanding the safety of explosives, and assessing the crashworthiness of vehicles. Within such applications it is often critical to accurately compute the evolution of the temperature because it is a state variable that affects the kinetics of competing active processes within the material (e.g., dislocation motion, phase transformation, decomposition). Depending on the selection of an independent state variable, e.g. temperature or entropy, the approach for computing temperature is well understood based on the thermodynamic framework attributed to Coleman and Noll. However, different computational codes used for modeling the dynamic response of materials adopt different independent state variables. In this work, two thermodynamically consistent strategies for computing the temperature of a coupled thermodynamic state are compared and implemented into two different Lagrangian computational codes. The equivalence of these two approaches is established through the numerical solutions of several test problems. Finally, the implication of various approximations made to each of these approaches within the literature are assessed in the context of uniaxial stress conditions (split Hopkinson pressure bar experiments) and uniaxial strain conditions (plate impact experiments). Here, it is shown that the temperature rate or energy partition approaches are equivalent when implemented in their complete forms, but that several common simplifying assumptions, that are warranted in the case of uniaxial stress, lead to significant errors in the resulting Hugoniot state for plate impact.

36 MATERIALS SCIENCE↗
DOE OSTI2014

The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations

The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem

This paper presents a preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. Starting from a simple analytic example, we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain. The preconditioner works by propagating information globally by concurrently sweeping in both directions over the subdomains, and can be interpreted as a coarse grid for the domain decomposition method. The resulting algorithm is shown to converge very fast, independently of the number of subdomains and frequency. The preconditioner has the advantage that, like the original Schwarz algorithm, it can be implemented as a matrix-free routine, with no additional preprocessing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Modeling of wave processes in blocky media with porous and fluid-saturated interlayers

The wave processes in blocky media are analyzed by applying different mathematical models, wherein the elastic blocks interact with each other via pliant interlayers with the complex mechanical properties. Four versions of constitutive equations are considered. In the first version, an elastic interaction between the blocks is simulated within the framework of linear elasticity theory, and the model of elastic–plastic interlayers is constructed to take into account the appearance of irreversible deformation of interlayers at short time intervals. In the second one, the effects of viscoelastic shear in the interblock interlayers are taken into the consideration using the Poynting–Thomson rheological scheme. In the third option, the model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. In the fourth case, the model of a fluid-saturated material with open pores is examined based on Biot's equations. The collapse of pores is modeled by the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact, which is used to describe the behavior of materials with the different resistance to tension and compression. It was shown that the thermodynamically consistent model is provided, which means that the energy balance equation is fulfilled for an entire blocky structure, where the kinetic and potential energy of the system is the sum of the kinetic and potential energies of the blocks and interlayers. Under numerical implementation of the interlayers models, the dissipationless finite difference Ivanov's method was used. The splitting method by spatial variables in the combination with the Godunov gap decay scheme was applied in the blocks. As a result, robust and stable computational algorithms are built and tested. Using MPI technology, the parallel software was designed for the modeling of wave processes in 2D setting. The numerical results are presented, discussed and future studies are outlined. - Highlights: • We model the propagation of waves in a blocky medium with compliant interlayers. • Models of porous and fluid saturated interlayers are proposed using Biot's approach. • A parallel computational algorithm is developed for supercomputers of cluster type. • Problems of instant rotation of central and boundary blocks are solved numerically. • Wave motions are compared in the cases of elastic and fluid-saturated interlayers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗