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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 OSTI2021

Risk-Averse Control of Fractional Diffusion with Uncertain Exponent

In this paper, we introduce and analyze a new class of optimal control problems constrained by elliptic equations with uncertain fractional exponents. We utilize risk measures to formulate the resulting optimization problem. We develop a functional analytic framework, study the existence of solution and rigorously derive the first-order optimality conditions. Additionally, we employ a sample-based approximation for the uncertain exponent and the finite element method to discretize in space. Further, we prove the rate of convergence for the optimal risk neutral controls when using quadrature approximation for the uncertain exponent and conclude with illustrative examples.

finite element method↗
DOE OSTI2016

MCNP6 Study of Spatial Fidelity Required for ROC Curve Convergence

The detection of special nuclear material at ports and borders is one of the primary missions of the Department of Homeland Security's (DHS) Domestic Nuclear Detection Office (DNDO). In support of this mission a large-scale modeling and simulation effort has been undertaken with the goal of providing a comprehensive tool-kit that addresses the complexity of problems involved with developing and maintaining technologies deployed to global nuclear detection architecture (GNDA) nodes. An important objective of DNDO's mission is to characterize detector system performance before deployment. In the effort to support this mission, the latest version of MCNP has been used to perform detectability studies of highly enriched uranium (HEU) to populate a database that will be used for the tool-kit. The characterization method used in the implementation of the database is the receiver operating characteristic (ROC). A ROC curve shows the limits of detectability of a given system as well as an overall metric of the efficacy of a detection system. This is accomplished by comparing total detector count distributions to the count distribution produced by background alone. For an in-depth explanation of the theory behind the MCNP production of ROC curves please refer to the paper, 'How To Use The Receiver Operating Characteristic Tally Option in MCNP6'. Building a useful database requires an expansive parameter space. The current tool-kit use nine parameters, which if varied with just 5 options each, results in nearly two million simulations to run. Depending on the set of parameters these simulations can take a few hours or a few weeks to complete. This computational cost necessitates the use of scaling algorithms to interpolate between the data contained in the database. The tool-kit employs a discrete event method to simulate the movement and detector response of special nuclear material (SNM) through a GNDA node. Given the nature of a discrete event simulation, constant motion of SNM must be split up in to discrete spatial detection points. The fidelity required of the spatial splitting to achieve a properly converged answer is investigated here for a neutron detection system. The detector used was a SNAP-3 neutron detector in front of a sphere of SNM in the presence of background radiation. A parameter study has been performed to determine the spatial fidelity required for ROC curve convergence for moving objects in a discrete event simulator. It appears that 5 points is the minimum number of detection points with 7 points needed for one of the parameter sets. The convergence worsens with increases to detection length but appears to improve with increasing detector distance. These results will help future work involving quantifying the accuracy based on given tolerances and parameters. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2013

ONERA-NASA Cooperative Effort on Liner Impedance Eduction

As part of a cooperation between ONERA and NASA, the liner impedance eduction methods developed by the two research centers are compared. The NASA technique relies on an objective function built on acoustic pressure measurements located on the wall opposite the test liner, and the propagation code solves the convected Helmholtz equation in uniform ow using a finite element method that implements a continuous Galerkin discretization. The ONERA method uses an objective function based either on wall acoustic pressure or on acoustic velocity acquired above the liner by Laser Doppler Anemometry, and the propagation code solves the linearized Euler equations by a discontinuous Galerkin discretization. Two acoustic liners are tested in both ONERA and NASA ow ducts and the measured data are treated with the corresponding impedance eduction method. The first liner is a wire mesh facesheet mounted onto a honeycomb core, designed to be linear with respect to incident sound pressure level and to grazing ow velocity. The second one is a conventional, nonlinear, perforate-over-honeycomb single layer liner. Configurations without and with ow are considered. For the nonlinear liner, the comparison of liner impedance educed by NASA and ONERA shows a sensitivity to the experimental conditions, namely to the nature of the source and to the sample width.

Primus, Julien↗
DOE OSTI2025

Machine-Learning-Based Multiscale Methods for 3D Modelling of Granular Materials by Incorporating History-Dependent State Variables

Over the past decades, the prevalence of machine learning (ML) methods has made the development of ML-based constitutive models for granular materials undoubtedly a popular subject. Numerous studies have been made to feature the loading path or history-dependent stress-strain response of granular media using neural networks. In this work, a novel finite element method (FEM)–ML multiscale approach was developed by incorporating internal variables to improve the simulation accuracy of 3D history-dependent granular materials for the first time. To this end, a surrogate constitutive model based on the single-step-based multi-layer perceptron (MLP) neural network was used to replace representative volume element (RVE) simulations conducted by the discrete element method (DEM) in the multiscale FEM–DEM approach. Although the prediction principle of the MLP aligns with the FEM algorithm, artificially added internal variables are required to differentiate the loading history. To address this issue, history variables associated with the Frobenius norm are proposed to be fed into the MLP coupled with the strain tensor to extract the history-dependent behaviour of granular assemblies. The developed FEM–ML approach was demonstrated in 3D conventional triaxial compression (CTC) simulations. Compared to the multiscale FEM–DEM approach, the proposed FEM–ML method exhibits a significantly improved computational efficiency.

granular materials↗
NASA NTRSDate not supplied

Trajectory Engineering with Modular Patched Conics for Entry Systems and TPS (TEMPEST)

Brief Presenter Biography (35 word limit): Bohdan Wesely is an Aerospace Engineer in the Entry Systems and Technology Division at Ames. He has worked on a variety of projects for NASA including integrated TPS (thermal protection system) flight hardware deliveries and testing services for commercial partners. Introduction: TEMPEST is a new trajectory analysis framework that is designed to fill the gap between dedicated flight mechanics tools and aerothermal and TPS sizing tools. The project started as an SJSU master’s thesis and has since evolved into a general conceptual design tool capable of studying a wide variety of entry problems. Development is ongoing in the Entry Systems and Technology Division at NASA ARC. Why TEMPEST: Space missions involving entry into a planetary atmosphere involve a series of unique requirements across multiple disciplines. Whether it is traditional entry descent and landing (EDL), or aerocapture, the vehicle must navigate to its target landing location or orbit state, and the TPS must protect the payload during entry. The design process typically involves iterative handoffs between various flight mechanics, flow solver, and material response level tools. During the early conceptual phase, a wide variety of feasible trajectories are simulated in a Monte Carlo scenario which broadly satisfy the mission or landing requirements. Next, computational fluid dynamics (CFD), direct simulation Monte Carlo (DSMC), and other flow solver analyses are performed at various key trajectory points to generate an aero-database, heating and TPS design requirements also emerge at this stage. At this point, with updated aerodynamics from the various flow solvers, trajectories can be re-run, this in turn can change the required freestream conditions for the CFD tools, and as a project progresses, these analyses converge, and uncertainty is reduced. However, there is always a “hand-off” occurring between two inherently coupled phenomena. Analysis Description: One of the goals with TEMPEST is to use a variety of first principles estimation methods coupled with an atmosphere model to predict vehicle aerothermodynamics across the entire flight regime while propagating a 3 or 6 degree of freedom (DoF) trajectory. Aerodynamics methods include modified Newtonian, Maxwell and Cercignani- Lampis-Lord (CLL) for continuum, transitional, and free molecular flow regimes. Aerothermodynamics include boundary layer and reference enthalpy methods, and Mutation++ for non-equilibrium chemistry modeling. TEMPEST is also capable of stitching multiple trajectory segments together to study mission scenarios like multi-pass aerocapture and aero-gravity assists. Most of the program is implemented in MATLAB using modern system objects, it relies on several C++ shared libraries for supporting tools like Gmsh, the Global Reference Atmospheric Model (GRAM), and Mutation++. The various first principles aerothermal estimation methods are discretized across either a structured axisymmetric panel mesh or an unstructured tri-mesh generated from an open-source tool such as Gmsh, this allows solutions on the same mesh to be compared across tools such as CB-Aero. CFD Coupling. A physics-aware, gaussian process CFD anchoring scheme is proposed to adjust the various first principles methods as a CFD database is populated. One goal for this anchoring module is to inform the project where CFD should be run. Full knowledge of the entire trajectory, atmosphere, and aerothermodynamics allows for easier identification of high sensitivity areas and uncertainty quantification. While the first principles effects are well known and proven accurate in existing tools such as CB- Aero and Cart3D, a physics aware CFD anchoring scheme increases tool credibility across a project lifecycle. Material Response Modeling. Correct TPS sizing is critical for optimizing mass for science payloads and ensuring mission success. The process typically involves a thermal analysis along the trajectory with surface heating environments as a boundary condition. Several design constraints are maximum bondline temperature and maximum recession with various margining techniques. The material response tool FIAT, developed out of NASA Ames, is currently being integrated into the TEMPEST environment. TPS recession, shape change, mass loss, and mass property alteration are all factors that can perturb an entry trajectory. For missions like Mars 2020, recession was minimal and was safely handled separately as a post process. For missions such as Jupiter Galileo with a high TPS mass fraction or asteroid entries, recession plays a major role. The proposed fully coupled scheme is to use an epoch-based approach where the trajectory integration is halted after a recession threshold, the energy balance and FIAT are solved at each panel, the mesh, aerodynamics, and mass properties are updated, and the trajectory continues. Several computational tradeoffs have been made during the development of TEMPEST to limit the cost of a single trajectory and preserve its utility as a conceptual, rapid iteration tool. Conclusion: Development of TEMPEST is ongoing and the project is still in its infancy. This talk aims to showcase its unique capabilities to support future NASA entry systems missions.

Bohdan O Wesely↗
NASA NTRS1996

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.

Gerhard, Craig Steven↗
DOE OSTI2013

Improved mesh based photon sampling techniques for neutron activation analysis

The design of fusion power systems requires analysis of neutron activation of large, complex volumes, and the resulting particles emitted from these volumes. Structured mesh-based discretization of these problems allows for improved modeling in these activation analysis problems. Finer discretization of these problems results in large computational costs, which drives the investigation of more efficient methods. Within an ad hoc subroutine of the Monte Carlo transport code MCNP, we implement sampling of voxels and photon energies for volumetric sources using the alias method. The alias method enables efficient sampling of a discrete probability distribution, and operates in 0(1) time, whereas the simpler direct discrete method requires 0(log(n)) time. By using the alias method, voxel sampling becomes a viable alternative to sampling space with the 0(1) approach of uniformly sampling the problem volume. Additionally, with voxel sampling it is straightforward to introduce biasing of volumetric sources, and we implement this biasing of voxels as an additional variance reduction technique that can be applied. We verify our implementation and compare the alias method, with and without biasing, to direct discrete sampling of voxels, and to uniform sampling. We study the behavior of source biasing in a second set of tests and find trends between improvements and source shape, material, and material density. Overall, however, the magnitude of improvements from source biasing appears to be limited. Future work will benefit from the implementation of efficient voxel sampling - particularly with conformal unstructured meshes where the uniform sampling approach cannot be applied. (authors)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Haar-Like Wavelets on Hierarchical Trees

Here, discrete wavelet methods, originally formulated in the setting of regularly sampled signals, can be adapted to data defined on a point cloud if some multiresolution structure is imposed on the cloud. A wide variety of hierarchical clustering algorithms can be used for this purpose, and the multiresolution structure obtained can be encoded by a hierarchical tree of subsets of the cloud. Prior work introduced the use of Haar-like bases defined with respect to such trees for approximation and learning tasks on unstructured data. This paper builds on that work in two directions. First, we present an algorithm for constructing Haar-like bases on general discrete hierarchical trees. Second, with an eye towards data compression, we present thresholding techniques for data defined on a point cloud with error controlled in the $L$ $\infty$ norm and in a Hölder-type norm. In a concluding trio of numerical examples, we apply our methods to compress a point cloud dataset, study the tightness of the $L$ $\infty$ error bound, and use thresholding to identify MNIST classifiers with good generalizability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification

The paper deals with the numerical solution of a compositional model describing compressible two-phase flow of a mixture composed of several components in porous media with species transfer between the phases. The mathematical model is formulated by means of the extended Darcy's laws for all phases, components continuity equations, constitutive relations, and appropriate initial and boundary conditions. The splitting of components among the phases is described using a new formulation of the local thermodynamic equilibrium which uses volume, temperature, and moles as specification variables. The problem is solved numerically using a combination of the mixed-hybrid finite element method for the total flux discretization and the finite volume method for the discretization of transport equations. A new approach to numerical flux approximation is proposed, which does not require the phase identification and determination of correspondence between the phases on adjacent elements. The time discretization is carried out by the backward Euler method. The resulting large system of nonlinear algebraic equations is solved by the Newton–Raphson iterative method. We provide eight examples of different complexity to show reliability and robustness of our approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Application of the GBFP Method to Electron Partial-Wave Expansion Elastic Scattering Differential Cross Sections Within the Geant4 Toolkit - Paper 69

Analog Monte Carlo simulation of electrons in complex material geometries is generally impractical because the long range Coulomb interactions result in highly peaked differential cross sections (DCS) for scattering and energy-loss and extremely small collision mean free paths (mfp). The condensed history (CH) Monte Carlo method attempts to alleviate this limitation by advancing electrons in fixed steps and sampling angular deflections and energy losses from precomputed distributions obtained from approximate solutions to the underlying transport equation that are valid only for thin layers. Though CH is efficient and is widely employed in production codes (ITS, MCNP, EGS, Geant), step size restrictions and inconsistent handling of material and free surface boundaries limit the ultimate accuracy possible with this approach, especially in applications to highly heterogeneous media. Recently proposed alternatives to the CH method, such as the Generalized Boltzmann Fokker-Planck (GBFP) method, restore the correct transport mechanics by simulating single events based on a Boltzmann transport equation but with efficiency and accuracy achieved through the use of reduced-physics interaction models. Motivated by Lewis theory, various moment-preserving strategies are employed in the GBFP approach to construct DCSs that are less singular, and with mfps shorter than analog. Specifically, the approximate cross sections are constructed to rigorously preserve a finite number of angular and energy-loss moments of the analog DCSs while all higher moments are approximated in terms of the exact lower moments. By systematically increasing the number of moments retained, any desired accuracy can be obtained for integrated quantities, such as dose, reflection and transmission yields, as well as distributed quantities such as energy and angular distributions. For relativistic Rutherford cross section models, the GBFP method has been demonstrated in Monte Carlo simulation to yield accuracy comparable to analog but at a fraction of the cost. One advantage of the GBFP approach is that angular deflection and energy-loss interactions depend only on Legendre moments and energy-loss moments and not the detailed form of the analog DCSs. This feature allows moment-preservation to be enforced through DCSs expressed as a superposition of discrete (i.e., using delta-functions) angular deflections and discrete energy losses. This promotes extremely efficient computation when compared to analog and completely continuous or hybrid discrete-continuous moment-based DCS reconstructions, while yielding highly accurate results for integrated and distributed quantities. In this paper, we demonstrate that the moment-preserving algorithms central to our fully discrete GBFP method can be readily extended to apply to tabulated DCS data, specifically to the partial-wave expansion (PWE) elastic scattering DCSs. Since data libraries for the PWE DCSs for energy and material combinations of interest can be prohibitively large, the GBFP method provides a means to reduce data storage requirements. We implemented our algorithm in the Geant4 Monte Carlo code and all numerical results are obtained using this implementation. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2025

An adaptive, data-driven multiscale approach for dense granular flows

The accuracy of coarse-grained continuum models of dense granular flows is limited by the lack of high-fidelity closure models for granular rheology. One approach to addressing this issue, referred to as the hierarchical multiscale method, is to use a high-fidelity fine-grained model to compute the closure terms needed by the coarse-grained model. The difficulty with this approach is that the overall model can become computationally intractable due to the high computational cost of the high-fidelity model. In this work, we describe a multiscale modeling approach for dense granular flows that utilizes neural networks trained using high-fidelity discrete element method (DEM) simulations to approximate the constitutive granular rheology for a continuum incompressible flow model. Our approach leverages an ensemble of neural networks to estimate predictive uncertainty that allows us to determine whether the rheology at a given point is accurately represented by the neural network model. Additional DEM simulations are only performed when needed, minimizing the number of additional DEM simulations required when updating the rheology. This adaptive coupling significantly reduces the overall computational cost of the approach while controlling the error. In addition, the neural networks are customized to learn regularized rheological behavior to ensure well-posedness of the continuum solution. We first validate the approach using two-dimensional steady-state and decelerating inclined flows. We then demonstrate the efficiency of our approach by modeling three-dimensional sub-aerial granular column collapse for varying initial column aspect ratios, where our multiscale method compares well with the computationally expensive computational fluid dynamics (CFD)-DEM simulation.

Dense granular flows↗
DOE OSTI2019

Quantification of Powder Spreading Process for Metal Additive Manufacturing

In powder bed additive manufacturing (AM), the powder spreading process can lead to inhomogeneity in layer height, porosity level, and particle size distribution. Hence, creating homogeneous layers is the first task for optimal printing. The conventional assessment methods for powder quality are limited to a measurement of powder morphology, flowability, particle size distribution, surface roughness, and packing density. However, those techniques may not be the most appropriate to quantify the powder bed characteristics since it is not able to capture local particle configuration and does not provide any vectoral information (e.g., arrangement of contacts between particles during spreading). In this project, we: 1) developed a powder spreading model using discrete element method (DEM) for multiple-layered process, 2) experimentally measure powder spreading dynamics including static angle of repose (AOR) and dynamic AOR in order to calibrate and subsequently validate the model, and 3) investigated the effect of particle spreading process parameters on spatial powder bed structure and quality using scalar (e.g., porosity, surface roughness, coordination number, and particle size distribution) and tensorial (e.g., directionality of inter-particle contacts) methods for a comprehensive quantification of powder bed.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Comparison of SERPENT and CASMO-5M for pressurized water reactors models

The objective of this work is to perform a preliminary assessment of the capability of SERPENT to generate cross sections for a PWR Beginning-of-Life (BOL) isothermal mini-core by comparing a SERPENT/PARCS solution with the results obtained using a CASMO-5M/PARCS approach. The PARCS code is used instead of the usual SIMULATE-3 to analyze the Swiss Reactors, because interfaces with PARCS already exist to obtain neutronic data from SERPENT. For the PWR configurations, the differences between CASMO-5M and SERPENT solutions are within 200 pcm at the assembly level and thus rather small when considering the deterministic transport method (energy/angular/space discretization) in CASMO-5M versus the stochastic treatment of SERPENT, the statistical uncertainties in the Monte-Carlo approach as well as the eventual differences in nuclear data used by both codes. At the 2D mini-core level, no major difference is observed when comparing PARCS run with CASMO-5M versus SERPENT cross sections. For the generation of kinetic parameters, non trivial differences are observed due both to the methods and the data used. For the relatively limited number of configurations considered, it is hard to make any definitive statement on the benefits of using Monte Carlo codes in terms of nuclear data generation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Assessment of model parameters in MFiX particle-in-cell approach

The limitations in numerical treatment of solids-phase in conventional methods like Discrete Element Model and Two-Fluid Model have facilitated the development of alternative techniques such as Particle-In-Cell (PIC). However, a number of parameters are involved in PIC due to its empiricism. In this work, global sensitivity analysis of PIC model parameters is performed under three distinct operating regimes common in chemical engineering applications, viz. settling bed, bubbling fluidized bed and circulating fluidized bed. Simulations were performed using the PIC method in Multiphase Flow with Interphase eXchanges (MFiX) developed by National Energy Technology Laboratory (NETL). A non-intrusive uncertainty quantification (UQ) based approach is applied using Nodeworks to first construct an adequate surrogate model and then identify the most influential parameters in each case. This knowledge will aid in developing an effective design of experiments and determine optimal parameters through techniques such as deterministic or statistical calibration.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2024

Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds

Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A New Physics-Based Modeling of Multiple Non-Planar Hydraulic Fractures Propagation

Because of the low permeability in shale plays, closely spaced hydraulic fractures and multilateral horizontal wells are generally required to improve production. Therefore, understanding the potential fracture interaction and stress evolution is critical in optimizing fracture/well design and completion strategy in multi-stage horizontal wells. In this paper, a novel fully coupled reservoir flow and geomechanics model based on the dual-lattice system is developed to simulate multiple non-planar fractures propagation. The numerical model from Discrete Element Method (DEM) is used to simulate the mechanics of fracture propagations and interactions, while a conjugate irregular lattice network is generated to represent fluid flow in both fractures and formation. The fluid flow in the formation is controlled by Darcy’s law, but within fractures it is simulated by using cubic law for laminar flow through parallel plates. Initiation, growth and coalescence of the microcracks will lead to the generation of macroscopic fractures, which is explicitly mimicked by failure and removal of bonds between particles from the discrete element network. We investigate the fracture propagation path in both homogeneous and heterogeneous reservoirs using the simulator developed. Stress shadow caused by the transverse fracture will change the orientation of principal stress in the fracture neighborhood, which may inhibit or alter the growth direction of nearby fracture clusters. However, the initial in-situ stress anisotropy often helps overcome this phenomenon. Under large in-situ stress anisotropy, the hydraulic fractures are more likely to propagate in a direction that is perpendicular to the minimum horizontal stress. Under small in-situ stress anisotropy, there is a greater chance for fractures from nearby clusters to merge with each other. Then, we examine the differences in fracture geometry caused by fracturing in cemented or uncemented wellbore. Moreover, the impact of intrinsic reservoir heterogeneity caused by the rock fabric and mineralogy on fracture nucleation and propagation paths is examined through a three-layered reservoir. Finally, we apply the method to a realistic heterogeneous dataset.

02 PETROLEUM↗
DOE OSTI2018

Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model

Here, we present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H 2 + in the singlet ungerade channels, and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of dissociative recombination for real molecular targets. The second, approximate, set of calculations employs a combination of multichannel quantum defect theory and frame transformation into a basis of Siegert pseudostates. The cross sections computed with the two methods are compared in detail for collision energies from 0 to 2 eV.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigid-body immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79-141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid-body equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the block-diagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗