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Results for “equation free projective integration”

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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17 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Verification of an improved equation-free projective integration method for neoclassical plasma-profile evolution in tokamak geometry

A brute-force, long-time gyrokinetic simulation of plasma profile evolution in magnetic fusion devices is not desirable due to large computational resource requirements and a possible accumulation of numerical error. The equation-free projective integration method of Keverekidis et al. [Commun. Math. Sci. 1(4), 715–762 (2003)] is one of the outstanding candidates in projecting micro-scale simulations to a longer timescale. However, its application to tokamak plasma has not been fruitful due to the appearance of spurious transient oscillations in the lifting process, which are present when the kinetic simulations are initialized with a simplified model distribution function and which make the kinetic simulations to deviate from the desired paths. In this work, a kinetically informed lifting algorithm is added to the equation-free projective integration method, which is then verified in the electrostatic gyrokinetic particle-in-cell code XGCa [R. Hager and C. S. Chang, Phys. Plasmas 23, 042503 (2016)] for a neoclassical ion heat transport problem with adiabatic electrons. This new lifting operator is demonstrated to control spurious transients, enabling an over four-times reduction in the overall computing time in the time-evolution of the ion temperature profile in an axisymmetric toroidal plasma. Further reduction in the computing time is found to be limited due to the stability properties of the linear least squares projective integrator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Projective multiscale time-integration for electrostatic particle-in-cell methods

The simulation of problems in kinetic plasma physics is often challenging due to strongly coupled phenomena across multiple scales. In this work, we propose a wavelet-based coarse-grained numerical scheme, based on the framework of Equation-Free Projective Integration, for a kinetic plasma system modeled by the Vlasov–Poisson equations. A kinetic particle-in-cell (PIC) code is used to simulate the meso scale dynamics for short time intervals. This allows the extrapolation over long time-steps of the behavior of a coarse wavelet-based discretization of the system. To validate the approach and the underlying concepts, we perform two 1D1V numerical experiments: nonlinear propagation and steepening of an ion wave, and the expansion of a plasma slab in vacuum. The direct comparisons to resolved PIC simulations show good agreement. We show that the speedup of the projective integration scheme over the full particle scheme scales linearly with the system size, demonstrating efficiency while taking into account fully kinetic, non-Maxwellian effects. This suggests that the approach is potentially interesting for kinetic plasma problems with a large separation of scales.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

First-principles free energies by hybrid thermodynamic integration for phase equilibria and fission product solubility in molten salts

The overarching goal of this research project is quantitative microscopic modeling of phase diagrams and solubility of actinides and lanthanide-fission products in molten salts for molten salt reactors. Application of molten salts as coolants and liquid fuels for next-generation reactors requires quantitative understanding of phase diagrams, equations of state and transport properties of binary and ternary molten salt mixtures, as well as solubility of fuel, fission products and reactor-wall corrosion products, but these remain beyond the reach of current first-principles computational techniques. We will address this fundamental capability gap using a novel hybrid framework for thermodynamic integration to directly predict absolute free energies of solid and molten salts at any specified conditions of composition, temperature and pressure. This framework will combine a hierarchy of first-principles, molecular dynamics and continuum techniques to deliver first-principles-level accuracy at a fraction of the computational cost of conventional ab initio molecular dynamics approaches. In particular, this technique is expected to provide first-principles accuracy, while off-loading most of the computational work on much less expensive classical molecular dynamics and continuum techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2021

ORNL FACE Tree Height, with data on height of a subset of trees measured every year, 1997-2009. Free-Air CO2 Enrichment (FACE) Experiment Synthesis Activities.

Height of 20 sweetgum trees in three rows of each of the plots in the Oak Ridge National Laboratory (ORNL) free-air CO2 enrichment (FACE) experiment was measured each year of the experiment (1997-2009). The trees were exposed to ambient or elevated CO2. Tree height data contribute to the overall project objectives to determine the integrated response of a deciduous forest to elevated CO2. Average tree height per plot was used in allometric equations to calculate tree dry mass each year and to test whether there were effects of elevated CO2 on canopy development. Height was derived from trigonometric calculation from measurements of horizontal distance of observer from the bole and the angles from observer’s eye to top and base of tree, using a Haglof sonic hypsometer. The data are presented in a csv file, with plot number in the first column, tree number in the second column, and height recorded to 0.1 m in 1997 to 2009 in remaining columns. Plots 1 and 2 had elevated CO2, and plots 3-5 were in ambient CO2. Missing data occur after the tree died. The experiment and the height measurement are described in: Norby, R. J., D. E. Todd, J. Fults, and D. W. Johnson. 2001. Allometric determination of tree growth in a CO2-enriched sweetgum stand. New Phytologist 150: 477-487. The ORNL FACE experiment is described at: https://richnorby.org/home/face-home/.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Topology optimization of additively manufactured fluidic components free of internal support structures

This report integrates projection-based approaches for implementing overhang constraints with fluid topology optimization to design additively manufactured fluidic components that do not require internal support structures. Internal support structures are challenging, potentially impossible to remove in complex fluid networks, yet would degrade fluidic performance if left within the part. This presents a major challenge in coupling topology optimization with additive manufacturing in the design of fluid components. The proposed approach leverages past work in overhang constraints for solid mechanics, including projection formulations and adjoint sensitivity analysis, and considers incompressible Navier–Stokes equations for laminar fluid flow. The approach is demonstrated on 2D and 3D fluid topology optimization problems to minimize pressure drop and constrain mass flow rates in pipes and manifolds. Resulting designs are crisp, logical, satisfy performance constraints, and satisfy overhang constraints, eliminating the need for internal support structures.

42 ENGINEERING↗
DOE OSTI2018

Internal Structure of Charged Particles in a GRT Gravitational Model

With the help of an exact solution of the Einstein and Maxwell equations, the internal structure of a multiply connected space of wormhole type with two unclosed static throats leading out of it into two parallel vacuum spaces or into one space is investigated in GRT for a free electric field and dust-like matter. The given geometry is considered as a particle–antiparticle pair with fundamental constants arising in the form of first integrals in the solution of the Cauchy problem – electric charges ±e of opposite sign in the throats and rest mass m{sub 0} – the total gravitational mass of the inner world of the particle in the throat. With the help of the energy conservation law, the unremovable rotation of the internal structure is included and the projection of the angular momentum of which onto the rotation axis is identified with the z-projection of the spin of the charged particle. The radius of 2-Gaussian curvature of the throat R* is identified with the charge radius of the particle, and the z-projection of the magnetic moment and the g-factor are found. The feasibility of the given gravitational model is confirmed by the found condition of independence of the spin quantum number of the electron and the proton s = 1/2 of the charge radius R* and the relativistic rest mass m* of the rotating throat, which is reliably confirmed experimentally, and also by the coincidence with high accuracy of the proton radius calculated in the model R{sub *p} = 0.8412·10{sup –13} cm with the value of the proton charge radius obtained experimentally by measuring the Lamb shift on muonic hydrogen. The electron in the given model also turns out to be a structured particle with radius R{sub *e} = 3.8617·10{sup –11} cm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation

We present a modified approach for simulating electronically nonadiabatic dynamics based on the Nakajima-Zwanzig generalized quantum master equation (GQME). The modified approach utilizes the fact that the Nakajima-Zwanzig formalism does not require casting the overall Hamiltonian in system-bath form, which is arguably neither natural nor convenient in the case of the Hamiltonian that governs nonadiabatic dynamics. Within the modified approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density operator is fully captured by a memory kernel super-operator. A methodology for calculating the memory kernel from projection-free inputs is developed. Simulating the electronic dynamics via the modified approach, with a memory kernel obtained using exact or approximate methods, can be more cost effective and/or lead to more accurate results than direct application of those methods. The modified approach is compared to previously proposed GQME-based approaches, and its robustness and accuracy are demonstrated on a benchmark spin-boson model with a memory kernel which is calculated within the Ehrenfest method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2011

Toward Realistic Dynamics of Rotating Orbital Debris, and Implications for Lightcurve Interpretation

Optical observations of rotating space debris near GEO contain important information on size, shape, composition, and rotational states, but these aspects are difficult to extract due to data limitations and the high number of degrees of freedom in the modeling process. For tri-axial rigid debris objects created by satellite fragmentations, the most likely initial rotation state has a large component of initial angular velocity directed along the intermediate axis of inertia, leading to large angular reorientations of the body on the timescale of the rotation period. This lends some support to the simplest possible interpretation of light curves -- that they represent sets of random orientations of the objects of study. However, effects of internal friction and solar radiation are likely to cause significant modification of rotation states within a time as short as a few orbital periods. In order to examine the rotational dynamics of debris objects under the influences of these effects, a set of seven first-order coupled equations of motion were assembled in state form: three are Euler equations describing the rates of change of the components of angular velocity in the body frame, and four describe the rates of change of the components of the unit quaternion. Quaternions are a four-dimensional extension of complex numbers that form a seamless, singularity-free representation of body orientation on S3. The Euler equations contain explicit terms describing torque from solar radiation in terms of spherical harmonics, and terms representing effects of a prescribed rate of internal friction. Numerical integrations of these equations of motion are being performed, and results will be presented. Initial tests show that internal friction without solar radiation torque leads to rotation about the maximum principal axis of inertia, as required, and solar radiation torque is expected to lead to spin-up of objects. Because the axis of maximum rotational inertia tends to be roughly coincident with the normal to the largest projected cross-sectional area, internal friction is expected to lead to reduced variation of light curve amplitudes at a given phase angle, but a large dependence of the same on phase angle. At a given phase angle, databases are generated which contain reflected intensities for comprehensive sets of equally-likely orientations, represented as unit quaternions. When projected onto three dimensions (S2) and color-coded by intensity, the set is depicted as points within a solid, semi-transparent unit sphere, within which all possible reflected intensities for an object at a given phase angle may be inspected simultaneously. Rotational sequences are represented by trajectories through the sphere. Databases are generated for each of a set of phase angles separately, forming a comprehensive dataset of reflected intensities spanning all object orientations and solar phase angles. Symmetries in the problem suggest that preferred rotation states are likely, defined relative to the object-sun direction in inertial space and relative to the maximum principal axis of inertia in the body coordinate system. Such rotation states may greatly simplify the problem of light curve interpretation by reducing the number of degrees of freedom in the problem.

Ojakangas, Gregory W.↗
NASA NTRS2006

A-Train Data Depot: Integrating and Visualizing Atmospheric Measurements Along the A-Train Tracks

The succession of US and international satellites that follow each other, seconds to minutes apart, across the local afternoon equator crossing is called the ATrain. The A-Train consists of the following satellites, in order of equator crossing: OCO, EOS Aqua, CloudSat, CALIPSO, PARASOL, and EOS Aura. Flying in such formation increases the number of observations, validates observations, and enables coordination between science observations, resulting in a more complete virtual science platform (Kelly, 2000) The goal of this project is to create the first ever A-Train virtual data portal/center, the A-Train Data Depot, to process, archive, access, visualize, analyze and correlate distributed atmosphere measurements from various A-Train instruments along A-Train tracks. The A-Train Data Depot (ATDD) will enable the free movement of remotely located A-Train data so that they are combined to create a consolidated vertical view of the Earth s Atmosphere along the A-Train tracks. Once the infrastructure of the ATDD is in place, it will be easily evolved to serve data from all A-Train data measurements: one stop shopping. The innovative approach of analyzing and visualizing atmospheric profiles along the platforms track (i.e., time) will be accommodated by reusing the GSFC Atmospheric Composition Data and Information Services Center (ACDISC) visualization and analysis tool, GIOVANNI, existing data reduction tools, on-line archwing for fast data access, and Cooperative Institute for Research in the Atmosphere (CRA) data co-registration tools. Initial measurements utilized include CALIPSO lidar backscatter, CloudSat radar reflectivity, clear air relative humidity, water vapor and temperature from AIRS, and cloud properties and aerosols from both MODIS. This will be followed by associated measurements from MLS, OMI, HIRDLS, and TES. Given the independent nature of instrument/platform development, the ATDD project has been met with many interesting challenges that, once resolved, will provide a much greater understanding of the relative flight dynamics and data co-registration of the suite of A-Train instruments, thus greatly increasing the accuracy of A-Train data analysis. Some of these challenges will be discussed. The project s resulting visualizations and analysis illustrate the importance of managing data so that measurements from various missions can be combined to enhance the understanding of the atmosphere. A-Train data management coordination, as performed here, is extremely significant in facilitating the A-Train science of clouds, precipitation, aerosol and chemistry.

Kempler, Steven↗
NASA NTRS2006

A-Train Data Depot: Integrating, Visualizing, and Extracting Cloudsat, CALIPSO, MODIS, and AIRS Atmospheric Measurements Along the A-Train Tracks

The succession of US and international Earth observing satellites that follow each other, seconds to minutes apart, across the local afternoon equator crossing is called the ATrain. The A-Train consists of the following satellites, in order of equator crossing: OCO, EOS Aqua, CloudSat, CALIPSO, PARASOL, and EOS Aura. Flying in such formation increases the number of observations, validates observations, and enables coordination between science observations, resulting in a more complete virtual science platform (Kelly, 2000). The goal of this project is to create the first ever A-Train virtual data portal/center, the A-Train Data Depot (ATDD), to process, archive, access, visualize, analyze and correlate distributed atmosphere measurements from various A-Train instruments along A-Train tracks. The ATDD will enable the free movement of remotely located A-Train data so that they are combined to create a consolidated vertical view of the Earth's Atmosphere along the A-Train tracks. Once the infrastructure of the ATDD is in place, it will be easily evolved to serve data from all A-Train data measurements: one stop shopping. The innovative approach of analyzing and visualizing atmospheric profiles along the platforms track (i.e., time) will be accommodated by reusing the GSFC Atmospheric Composition Data and Information Services Center (ACDISC) visualization and analysis tool, GIOVANNI, existing data reduction tools, on-line archiving for fast data access, access to remote data without unnecessary data transfers, and data retrieval by users finding data desirable for further study. Initial measurements utilized include CALIPSO lidar backscatter, CloudSat radar reflectivity, clear air relative humidity, water vapor and temperature from AIRS, and cloud properties and aerosols from both MODIS. This will be foilowed by associated measurements from TVILS, =MI, HIRDLS, sad TES. Given the independent nature of instrumentlplatform development, the ATDD project has been met with many interesting challenges that, once resolved, will provide a much greater understanding of the relative flight dynamics and data co-registration of the suite of A-Train instruments, thus greatly increasing the accuracy of A-Train data analysis. Some of these challenges will be illustrated and discussed. The project's early visualizations and analysis efforts illustrate the importance of managing data so that measurements from various missions can be combined to enhance the understanding of the atmosphere. A-Train data management coordination, as performed here, is extremely significant in facilitating the A-Train science of clouds, precipitation, aerosol and chemistry.

Kempler, Steven↗
NASA NTRS1987

A numerical study of three-dimensional vortex breakdown

A numerical simulation of bubble-type vortex breakdown using a unique discrete form of the full 3-D, unsteady incompressible Navier-Stokes equations was performed. The Navier-Stokes equations were written in a vorticity-velocity form and the physical problem was not restricted to axisymmetric flow. The problem was parametized on a Rossby- Reynolds-number basis. Utilization of this parameter duo was shown to dictate the form of the free-field boundary condition specification and allowed control of axial breakdown location within the computational domain. The structure of the breakdown bubble was studied through time evolution plots of planar projected velocity vectors as well as through plots of particle traces and vortex lines. These results compared favorably with previous experimental studies. In addition, profiles of all three velocity components are presented at various axial stations and a Fourier analysis was performed to identify the dominant circumferential modes. The dynamics of the breakdown process were studied through plots of axial variation of rate of change of integrated total energy and rate of change of integrated enstrophy, as well as through contour plots of velocity, vorticity and pressure.

Spall, Robert E.↗
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Direct numerical simulations and modeling of a spatially-evolving turbulent wake

Understanding of turbulent free shear flows (wakes, jets, and mixing layers) is important, not only for scientific interest, but also because of their appearance in numerous practical applications. Turbulent wakes, in particular, have recently received increased attention by researchers at NASA Langley. The turbulent wake generated by a two-dimensional airfoil has been selected as the test-case for detailed high-resolution particle image velocimetry (PIV) experiments. This same wake has also been chosen to enhance NASA's turbulence modeling efforts. Over the past year, the author has completed several wake computations, while visiting NASA through the 1993 and 1994 ASEE summer programs, and also while on sabbatical leave during the 1993-94 academic year. These calculations have included two-equation (K-omega and K-epsilon) models, algebraic stress models (ASM), full Reynolds stress closure models, and direct numerical simulations (DNS). Recently, there has been mutually beneficial collaboration of the experimental and computational efforts. In fact, these projects have been chosen for joint presentation at the NASA Turbulence Peer Review, scheduled for September 1994. DNS calculations are presently underway for a turbulent wake at Re(sub theta) = 1000 and at a Mach number of 0.20. (Theta is the momentum thickness, which remains constant in the wake of a two dimensional body.) These calculations utilize a compressible DNS code written by M. M. Rai of NASA Ames, and modified for the wake by J. Cimbala. The code employs fifth-order accurate upwind-biased finite differencing for the convective terms, fourth-order accurate central differencing for the viscous terms, and an iterative-implicit time-integration scheme. The computational domain for these calculations starts at x/theta = 10, and extends to x/theta = 610. Fully developed turbulent wake profiles, obtained from experimental data from several wake generators, are supplied at the computational inlet, along with appropriate noise. After some adjustment period, the flow downstream of the inlet develops into a fully three-dimensional turbulent wake. Of particular interest in the present study is the far wake spreading rate and the self-similar mean and turbulence profiles. At the time of this writing, grid resolution studies are underway, and a code is being written to calculate turbulence statistics from these wake calculations; the statistics will be compared to those from the ongoing PIV wake measurements, those of previous experiments, and those predicted by the various turbulence models. These calculations will lead to significant long-term benefits for the turbulence modeling effort. In particular, quantities such as the pressure-strain correlation and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. Present turbulence models do a very good job at prediction of the shape of the mean velocity and Reynolds stress profiles in a turbulent wake, but significantly underpredict the magnitude of the stresses and the spreading rate of the wake. Thus, the turbulent wake is an ideal flow for turbulence modeling research. By careful comparison and analysis of each term in the modeled Reynolds stress equations, the DNS data can show where deficiencies in the models exist; improvements to the models can then be attempted.

Cimbala, John M.↗
NASA NTRS2013

Engineering Evaluation of International Low Impact Docking System Latch Hooks

The international Low Impact Docking System (iLIDS) provides a structural arrangement that allows for visiting vehicles to dock with the International Space Station (ISS) (Fig 1). The iLIDS docking units are mechanically joined together by a series of active and passive latch hooks. In order to preserve docking capability at the existing Russian docking interfaces, the iLIDS latch hooks are required to conform to the existing Russian design. The latch hooks are classified as being fail-safe. Since the latch hooks are fail-safe, the hooks are not fracture critical and a fatigue based service life assessment will satisfy the structural integrity requirements. Constant amplitude fatigue testing to failure on four sets of active/passive iLIDS latch hooks was performed at load magnitudes of 10, 11, and 12 kips. Failure analysis of the hook fatigue failures identified multi-site fatigue initiation that was effectively centered about the hook mid-plane (consistent with the 3D model results). The fatigue crack initiation distribution implies that the fatigue damage accumulation effectively results in a very low aspect ratio surface crack (which can be simulated as thru-thickness crack). Fatigue damage progression resulted in numerous close proximity fatigue crack initiation sites. It was not possible to determine if fatigue crack coalescence occurs during cyclic loading or as result of the fast fracture response. The presence of multiple fatigue crack initiation sites on different planes will result in the formation of ratchet marks as the cracks coalesce. Once the stable fatigue crack becomes unstable and the fast fracture advances across the remaining ligament and the plane stress condition at a free-surface will result in failure along a 45 deg. shear plane (slant fracture) and the resulting inclined edge is called a shear lip. The hook thickness on the plane of fatigue crack initiation is 0.787". The distance between the shear lips on this plane was on the order of 0.48" and it was effectively centered about the mid-plane of the section. The numerous ratchet marks between the shear lips on the fracture initiation plane are indicative of multiple fatigue initiation sites within this region. The distribution of the fatigue damage about the centerline of the hook is consistent with the analytical results that demonstrate peak stress/strain response at the mid-plane that decreases in the direction of the hook outer surfaces. Scanning electron microscope images of the failed sections detected fatigue crack striations in close proximity to the free surface of the hook radius. These findings were documented at three locations on the fracture surface : 1) adjacent to the left shear lip, 2) adjacent to the right shear lip, and 3) near the centerline of the section. The features of the titanium fracture surface did not allow for a determination of a critical crack size via identification of the region where the fatigue crack propagation became unstable. The fracture based service life projections where benchmarked with strain-life analyses. The strainrange response in the hook radius was defined via the correlated finite element models and the modified method of universal slopes was incorporated to define the strain-life equation for the titanium alloy. The strain-life assessment confirmed that the fracture based projections were reasonable for the loading range of interest. Based upon the analysis and component level fatigue test data a preliminary service life capability for the iLIDS active and passive hooks of 2 lifetimes is projected (includes a scatter factor of 4).

Martinez, J.↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

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