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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.

Pan, Wenxiao↗
DOE OSTI2017

Numeric invariants from multidimensional persistence

Topological data analysis is the study of data using techniques from algebraic topology. Often, one begins with a finite set of points representing data and a “filter” function which assigns a real number to each datum. Using both the data and the filter function, one can construct a filtered complex for further analysis. For example, applying the homology functor to the filtered complex produces an algebraic object known as a “one-dimensional persistence module”, which can often be interpreted as a finite set of intervals representing various geometric features in the data. If one runs the above process incorporating multiple filter functions simultaneously, one instead obtains a multidimensional persistence module. Unfortunately, these are much more difficult to interpret. In this article, we analyze the space of multidimensional persistence modules from the perspective of algebraic geometry. First we build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence instead of one-dimensional persistence. Fruthermore, we argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Finally, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data. This paper extends the results of Adcock et al. (Homol Homotopy Appl 18(1), 381–402, 2016) by constructing numeric invariants from the computation of a multidimensional persistence module as given by Carlsson et al. (J Comput Geom 1(1), 72–100, 2010).

58 GEOSCIENCES↗
DOE OSTI2015

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

We present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Jüttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviours that do not exist in the nonrelativistic case. The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

High-Fidelity Numerical Wave Tank Verification & Validation Study: Wave Generation Through Paddle Motion: Preprint

This paper presents a numerical benchmark study of wave propagation due to a paddle motion using different high-fidelity numerical models, which are capable of replicating the nearly actual physical wave tank testing. A full time series of the measured wave generation paddle motion which was used to generate wave propagation in the physical wave tank will be utilized in each of the models contributed by IEA OES Task 10's participants, which includes both computational fluid dynamics (CFD) and smooth hydrodynamic particle (SPH). The high-fidelity simulations of the physical wave testcase will allow for the evaluation of the initial transient effects from wave ramp-up and its evolution in the wave tank over time for two representative regular waves with varying levels of nonlinearity. A couple of interesting metrics like the predicted wave surface elevation at select wave probes, wave period, and phase-shift in time will be assessed to evaluate the relative accuracy of numerical models versus experimental data within specified time intervals. These models will serve as a guide for modelers in the wave energy community and provide a base case to allow further and more detailed numerical modeling of the fixed Kramer Sphere Cases under wave excitation force wave tank testing.

HYDRO ENERGY,TIDAL AND WAVE POWER↗
DOE OSTI2019

India National Gas Hydrate Program Expedition 02 Summary of Scientific Results: Numerical Simulation of Reservoir Response to Depressurization

The India National Gas Hydrate Program Expedition 02 (NGHP-02) discovered gas hydrate at high saturation in sand reservoirs at several sites in the deepwater Bay of Bengal. To assess the potential response of those deposits to scientific depressurization experiments, comprehensive geologic models were constructed to enable numerical simulation for two sites. Both sites (NGHP-02-09 and NGHP-02-16) feature thick sequences of thinly-interbedded reservoir and non-reservoir facies at sub-seafloor depths less than 300m and sub-sea depths of 2400m or more. These settings pose significant challenges to current modeling capabilities. First, the thinly-interbedded reservoir architecture complicates the determination of basic reservoir parameters from both log and core data due to measurement resolution issues. Secondly, the fine scale variation in sediment properties imparts great contrasts in key parameters over very short distances, creating high gradients at multiple scales and varying orientations that necessitate careful design of high-definition simulation grids. Thirdly, the deposits include internal sources of water, as well as a range of complex boundary conditions, including variable permeability within the overlying mud-rich “seals,” that complicate reservoir depressurization. Lastly, because of the unique combination of great water depth and relatively shallow sub-seafloor depth: models designed to maximize the dissociation rate impose large pressure drawdowns on relatively low-strength sediments. This condition renders the proper evaluation and integration of the geomechanical response to hydrate dissociation critical. In this report, we review the history of gas hydrate reservoir simulation, discuss methods for creating geologic input models, and summarize the key findings and implications of the collaborative NGHP-02 numerical simulation effort. Together, the studies confirm the viability of the modeled accumulations for scientific testing and identify key challenges related to the selection of specific test sites and the design of test wells.

Boswell, Ray↗
DOE OSTI2024

Large‐Area, High‐Numerical‐Aperture, Freeform Metasurfaces

Abstract Nanophotonic devices are optical platforms capable of unprecedented wavefront control. To push the limits of experimental device performance, scalable design methodologies that combine the simplicity and fabricability of conventional design paradigms with the extended capabilities of freeform optimization are required. A novel gradient‐based design framework for large‐area freeform metasurfaces is introduced in which nonlocal interactions between simply shaped nanostructures, placed on an irregular lattice, are tailored to produce high‐order hybridized modes that support customizable large‐angle scattering profiles. Utilizing this approach, multifunctional super‐dispersive metalenses are designed and experimentally demonstrated. The approach to high‐numerical‐aperture radial metalenses capable of diffraction limited focusing and the generation of donut‐shaped point spread functions is also extended. It is anticipated that these concepts will have utility in super‐resolution microscopy, particle trapping, additive manufacturing, and metrology applications that require ultra‐high numerical apertures.

Optics↗
DOE OSTI2016

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Numerical simulations of membrane distillation systems with actively heated membranes

Membrane distillation (MD) is a thermal desalination process that is gaining attention for treating hypersaline brines. One recent approach uses composite membranes with a thermally conductive layer that delivers heat to the membrane–feed interface, where it drives evaporation. Though this increases single-pass recovery, it comes with the challenge of promoting lateral heat conduction through the thin membrane. Herein, we develop a 3D, computational fluid dynamics (CFD) model that simulates conjugate heat, mass, and momentum transport in the feed channel and composite membrane. We then use the CFD to verify a simpler numerical model that approximates the feed velocity field analytically. We validate the numerical model experimentally, and use it to investigate the impacts of the conductive layer thickness, feed channel geometry, and operating conditions on temperature and concentration polarization, permeate production, and specific energy consumption. Overall, we find that lateral heating increases permeate production at the expense of increased concentration polarization. In extreme cases, the concentration increases more than four-fold along the membrane surface. Furthermore, we show however, that the feed flow rate and conductive layer thickness can be tailored to mitigate concentration polarization, for only a small reduction in permeate production.

42 ENGINEERING↗
DOE OSTI2014

Chaoticity threshold in magnetized plasmas: Numerical results in the weak coupling regime

The present paper is a numerical counterpart to the theoretical work [Carati et al., Chaos 22, 033124 (2012)]. We are concerned with the transition from order to chaos in a one-component plasma (a system of point electrons with mutual Coulomb interactions, in a uniform neutralizing background), the plasma being immersed in a uniform stationary magnetic field. In the paper [Carati et al., Chaos 22, 033124 (2012)], it was predicted that a transition should take place when the electron density is increased or the field decreased in such a way that the ratio ω{sub p}/ω{sub c} between plasma and cyclotron frequencies becomes of order 1, irrespective of the value of the so-called Coulomb coupling parameter Γ. Here, we perform numerical computations for a first principles model of N point electrons in a periodic box, with mutual Coulomb interactions, using as a probe for chaoticity the time-autocorrelation function of magnetization. We consider two values of Γ (0.04 and 0.016) in the weak coupling regime Γ ≪ 1, with N up to 512. A transition is found to occur for ω{sub p}/ω{sub c} in the range between 0.25 and 2, in fairly good agreement with the theoretical prediction. These results might be of interest for the problem of the breakdown of plasma confinement in fusion machines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Fundamental form of the electrostatic δf-PIC algorithm and discovery of a converged numerical instability

The δf particle-in-cell algorithm has been a useful tool in studying the physics of plasmas, particularly turbulent magnetized plasmas in the context of gyrokinetics. The reduction in noise due to not having to resolve the full distribution function indicates an efficiency advantage over the standard (“full-f”) particle-in-cell. Despite its successes, the algorithm behaves strangely in some circumstances. In this work, we document a fully resolved numerical instability that occurs in the simplest of multiple-species test cases: the electrostatic Ω{sub H} mode. There is also a poorly understood numerical instability that occurs when one is under-resolved in particle number, which may require a prohibitively large number of particles to stabilize. Both of these are independent of the time-stepping scheme, and we conclude that they exist if the time advancement were exact. The exact analytic form of the algorithm is presented, and several schemes for mitigating these instabilities are also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

On numerical considerations for modeling reactive astrophysical shocks

Simulating detonations in astrophysical environments is often complicated by numerical approximations to shock structure. A common prescription to ensure correct detonation speeds and associated quantities is to prohibit burning inside the numerically broadened shock. We have performed a series of simulations to verify the efficacy of this approximation and to understand how resolution and dimensionality might affect its use. Our results show that in one dimension, prohibiting burning in the shock is important wherever the carbon burning length is not resolved, in keeping with the results of Fryxell et al. In two dimensions, we find that the prohibition of shock burning effectively inhibits the development of cellular structure for all but the most highly resolved cases. We discuss the possible impacts this outcome may have on sub-grid models and detonation propagation in models of Type Ia supernovae, including potential impacts on observables.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Variations of characteristic time scales in rotating stratified turbulence using a large parametric numerical study

In this work, we study rotating stratified turbulence (RST) making use of numerical data stemming from a large parametric study varying the Reynolds, Froude and Rossby numbers, Re, Fr and Ro in a broad range of values. The computations are performed using periodic boundary conditions on grids of 10243 points, with no modeling of the small scales, no forcing and with large-scale random initial conditions for the velocity field only, and there are altogether 65 runs analyzed in this paper. The buoyancy Reynolds number defined as R B = ReFr 2 varies from negligible values to ≈ 105, approaching atmospheric or oceanic regimes. This preliminary analysis deals with the variation of characteristic time scales of RST with dimensionless parameters, focusing on the role played by the partition of energy between the kinetic and potential modes, as a key ingredient for modeling the dynamics of such flows. We find that neither rotation nor the ratio of the Brunt-Väisälä frequency to the inertial frequency seem to play a major role in the absence of forcing in the global dynamics of the small-scale kinetic and potential modes. Specifically, in these computations, mostly in regimes of wave turbulence, characteristic times based on the ratio of energy to dissipation of the velocity and temperature fluctuations, T V and T P , vary substantially with parameters. Their ratio γ=T V /T P follows roughly a bell-shaped curve in terms of Richardson number Ri. It reaches a plateau --on which time scales become comparable, γ≈0.6 -- when the turbulence has significantly strengthened, leading to numerous destabilization events together with a tendency towards an isotropization of the flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Numerical and experimental evaluation of mechanical performance of the multifunctional energy storage composites

This work presents numerical simulation methods to model the mechanical behavior of the multifunctional energy storage composites (MESCs), which consist of a stack of multiple thin battery layers reinforced with through-the-hole polymer rivets and embedded inside carbon fiber composite laminates. MESC has been demonstrated through earlier experiments on its exceptional behavior as a structural element as well as a battery. However, the inherent complex infrastructure of the MESC design has created significant challenges in simulation and modeling. A novel homogenization technique was adopted to characterize the multi-layer properties of battery material using physics-based constitutive equations combined with nonlinear deformation theories to handle the interface between the battery layers. Second, mechanical damage and failure modes among battery materials, polymer reinforcements, and carbon fiber-polymer interfaces were characterized through appropriate models and experiments. The model of MESCs has been implemented in a commercial finite element code in ABAQUS. A comparison of structural response and failure modes from numerical simulations and experimental tests are presented. The results of the study showed that the predictions of elastic and damage responses of MESCs at various loading conditions agreed well with the experimental data. © 2021

Materials Science↗
NASA NTRS1998

Spurious Numerical Oscillations in Numerical Simulation of Supersonic Flows Using Shock Capturing Schemes

The numerical simulation of transitional and turbulent processes in hypersonic boundary layers often involves a physical process of a shock-disturbance wave interaction in complex two-dimensional and three-dimensional flow fields. For such simulations, it is required that there be a high order of accuracy in capturing both the shock and the small disturbances. The purpose of this paper is to evaluate the viability of using high order shock capturing schemes to track small disturbances in a multi-dimensional steady hypersonic flow. The numerical methods that are to be studied are the Total Variation Diminishing (TVD) scheme, and Essentially Non-Oscillatory (ENO) scheme. This paper shows that the presence of numerical oscillations in the flow field solution may drastically hinder any attempt at tracking the propagation of any physical disturbances. It has been found that the numerical oscillations that exist for shock capturing methods may be significant enough to pollute a flow field containing small physical disturbances. The effects of the refinement of the grid do not reduce the oscillations, but rather they decrease the wavelength of the oscillations. It is shown that by aligning the shock with the grid, the amplitude of these spurious oscillations may be greatly reduced.

Lee, Theodore K.↗
DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2015

Impact of numerics on the predictive capabilities of reacting flow LES

Combustors in modern aerospace propulsion systems are highly optimized devices and further enhancements to their performance will require advanced predictive modeling techniques. The LES approach has potential to be such a technique, but demonstration of its true predictive capability remains a challenge. In this paper, a methodical study is performed to assess the impact of numerical error on the predictive capabilities of LES and to distinguish it from error arising from physical modeling. Four codes are employed to simulate the bluff body stabilized flame experiment of Volvo Flygmotor AB. The physical models (governing equations and sub-grid models) are kept identical between the codes so that the physical modeling error is the same. For the same reason, computational grids are also kept identical since the sub-grid models are grid dependent. Results indicate that all codes produce a very similar solution for the non-reacting flow in terms of large scale unsteady vortex shedding behavior, mean profiles and second order turbulence statistics, on a suitably refined grid. This solution is also very close to the experimentally observed behavior of the flow. In contrast, for the reacting case, solutions from the various codes exhibit significant differences when analyzed under the same metrics and with similar or even finer grid resolution than that used for the non-reacting case. These differences are large enough to change the macroscopic behavior of the flow, e.g. some codes predict symmetric vortex shedding while others predict asymmetric shedding and some codes show strong recirculation zones while others show stagnant regions behind the bluff body. It is also shown that none of the solutions truly predicts the experimentally observed flow. Given that the physical sub-grid models and computational grids are the same in all the simulations, the inconsistency between results points to a significant impact of numerical methods and, hence, numerical error. The need for mitigation of this impact is highlighted, along with the need for metrics detailing how LES should be applied to reacting flows. It is suggested that both of these issues should be the focus of future work.

Energy & Fuels↗