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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials

Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.

36 MATERIALS SCIENCE↗
NASA NTRS1983

Simulation of turbulent shear flows at Stanford and NASA-Ames - What can we do and what have we learned?

The capabilities and limitations of large eddy simulation (LES) and full turbulence simulation (FTS) are outlined. It is pointed out that LES, although limited at the present time by the need for periodic boundary conditions, produces large-scale flow behavior in general agreement with experiments. What is more, FTS computations produce small-scale behavior that is consistent with available experiments. The importance of the development work being done on the National Aerodynamic Simulator is emphasized. Studies at present are limited to situations in which periodic boundary conditions can be applied on boundaries of the computational domain where the flow is turbulent.

Reynolds, W. C.↗
NASA NTRS2009

Molecular Modeling for Calculation of Mechanical Properties of Epoxies with Moisture Ingress

Atomistic models of epoxy structures were built in order to assess the effect of crosslink degree, moisture content and temperature on the calculated properties of a typical representative generic epoxy. Each atomistic model had approximately 7000 atoms and was contained within a periodic boundary condition cell with edge lengths of about 4 nm. Four atomistic models were built with a range of crosslink degree and moisture content. Each of these structures was simulated at three temperatures: 300 K, 350 K, and 400 K. Elastic constants were calculated for these structures by monitoring the stress tensor as a function of applied strain deformations to the periodic boundary conditions. The mechanical properties showed reasonably consistent behavior with respect to these parameters. The moduli decreased with decreasing crosslink degree with increasing temperature. The moduli generally decreased with increasing moisture content, although this effect was not as consistent as that seen for temperature and crosslink degree.

Clancy, Thomas C.↗
DOE OSTI2021

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗
DOE OSTI2020

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ* scales weakly with system size, i.e., the dependence of ℓ* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim L→∞ (ℓ*/L) = 0. In particular, for (2+1)-dimensional interfaces ℓ* is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. Overall, this weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Developing and testing capabilities for simulating cases with heterogeneous land/water surfaces in a novel atmospheric large eddy simulation code

Large eddy simulations (LES) are the primary computational tool used to simulate high Reynolds number three-dimensional turbulent flows. In the context of earth system sciences, particularly atmospheric science, LES are uniquely able to resolve the scales of atmospheric motion that are key for building process-level understanding of boundary layer turbulence, atmosphere-surface interaction, clouds, and cloud-aerosol-chemistry interaction, and are a core limited-area modeling capability. Increasing demands are being placed on LES code bases as growing high performance computing resources allow LES to address a wider range of scientific problems. In addition, LES are emerging as a source of high-quality machine learning training data. These demands necessitate an agile and extensible code base that allows the model to quickly adapt to emergent needs. However, LES have largely relied on legacy Fortran code bases that lack flexibility. A new, Python-based LES capability called Predicting INteractions of Aerosol and Clouds in Large Eddy Simulation (PINACLES) has been developed as part of the Department of Energy’s Earth System Model Development (ESMD) program area’s Enabling Aerosol-cloud interactions at Global convection-permitting scalES (EAGLES) project. PINACLES was developed from the ground up with a philosophy of maximizing scientific throughput, by attempting to optimize for both model throughput and software extensibility. The initial development of PINACLES delivered a state-of-the-art idealized LES capability solving the non-hydrostatic anelastic equations of motion with doubly periodic boundary conditions and idealized homogenous surface boundary conditions. Here we provide a final report on the outcomes of a fiscal year 2021 Seed Laboratory Directed Research Project that extended PINACLES in two key ways. First, PINACLES was coupled to a state-of-the-art land surface model enabling it to simulate spatially inhomogeneous land-atmosphere interactions that are known to control key atmospheric processes. Second, the dynamical core of PINACLES was modified to permit non-periodic boundary conditions. This model enhancement enables simulation of realistic cases with boundary conditions prescribed from atmospheric reanalysis and enables nested simulations conducted on a hierarchy of computational domains with increasing resolution. Together, these extensions to PINACLES make it a formidable modeling capability and expand its potential application to diverse components of DOE’s atmospheric science portfolio.

42 ENGINEERING↗
DOE OSTI2021

Finite-size correction for slab supercell calculations of materials with spontaneous polarization

Abstract The repeated slab approach has become a de facto standard to accurately describe surface properties of materials by density functional theory calculations with periodic boundary conditions. For materials exhibiting spontaneous polarization, we show that the conventional scheme of passivation with pseudo hydrogen is unable to realize a charge-neutral surface. The presence of a net surface charge induces via Gauss’s law a macroscopic electric field through the slab and results in poor size convergence with respect to the thickness of the slab. We propose a modified passivation method that accounts for the effect of spontaneous polarization, describes the correct bulk limits and boosts convergence with respect to slab thickness. The robustness, reliability, and superior convergence of energetics and electronic structure achieved by the proposed method are demonstrated using the example of polar ZnO surfaces.

Chemistry↗
NASA NTRS1992

Direct numerical simulation of instabilities in parallel flow with spherical roughness elements

Results from a direct numerical simulation of laminar flow over a flat surface with spherical roughness elements using a spectral-element method are given. The numerical simulation approximates roughness as a cellular pattern of identical spheres protruding from a smooth wall. Periodic boundary conditions on the domain's horizontal faces simulate an infinite array of roughness elements extending in the streamwise and spanwise directions, which implies the parallel-flow assumption, and results in a closed domain. A body force, designed to yield the horizontal Blasius velocity in the absence of roughness, sustains the flow. Instabilities above a critical Reynolds number reveal negligible oscillations in the recirculation regions behind each sphere and in the free stream, high-amplitude oscillations in the layer directly above the spheres, and a mean profile with an inflection point near the sphere's crest. The inflection point yields an unstable layer above the roughness (where U''(y) is less than 0) and a stable region within the roughness (where U''(y) is greater than 0). Evidently, the instability begins when the low-momentum or wake region behind an element, being the region most affected by disturbances (purely numerical in this case), goes unstable and moves. In compressible flow with periodic boundaries, this motion sends disturbances to all regions of the domain. In the unstable layer just above the inflection point, the disturbances grow while being carried downstream with a propagation speed equal to the local mean velocity; they do not grow amid the low energy region near the roughness patch. The most amplified disturbance eventually arrives at the next roughness element downstream, perturbing its wake and inducing a global response at a frequency governed by the streamwise spacing between spheres and the mean velocity of the most amplified layer.

Deanna, R. G.↗
DOE OSTI2021

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Scalable Simulation of Pressure Gradient-Driven Transport of Rarefied Gases in Complex Permeable Media Using Lattice Boltzmann Method

Accurate representations of slip and transitional flow regimes present a challenge in the simulation of rarefied gas flow in confined systems with complex geometries. In these regimes, continuum-based formulations may not capture the physics correctly. This work considers a regularized multi-relaxation time lattice Boltzmann (LB) method with mixed Maxwellian diffusive and halfway bounce-back wall boundary treatments to capture flow at high Kn. The simulation results are validated against atomistic simulation results from the literature. We examine the convergence behavior of LB for confined systems as a function of inlet and outlet treatments, complexity of the geometry, and magnitude of pressure gradient and show that convergence is sensitive to all three. The inlet and outlet boundary treatments considered in this work include periodic, pressure, and a generalized periodic boundary condition. Compared to periodic and pressure treatments, simulations of complex domains using a generalized boundary treatment conserve mass but require more iterations to converge. Convergence behavior in complex domains improves at higher magnitudes of pressure gradient across the computational domain, and lowering the porosity deteriorates the convergence behavior for complex domains.

42 ENGINEERING↗
NASA NTRS1993

On the spline-based wavelet differentiation matrix

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

Jameson, Leland↗
NASA NTRS1996

On the Generation of Turbulent Inflow Conditions for Boundary Layer Simulations

Turbulent flows that exhibit inhomogeneities in the streamwise direction pose a particular challenge to numerical simulation approaches due to the need to prescribe time-dependent turbulent inflow conditions. In most cases the flow downstream is more or less 'driven' by the conditions at the inlet, making it necessary to specify realistic turbulent fluctuations that are in equilibrium with the assumed mean flow. This requirement often dictates that the inflow data should satisfy the Navier-Stokes equations, which in turn implies that an independent simulation be used to generate them. Detailed simulations for the purpose of creating inflow conditions can be costly and thus certain levels of approximation are desirable. In this paper we shall focus on an approximate yet accurate method for generating inflow conditions for spatially-developing boundary layer simulations. The proposed method is essentially a simplification of the method of Spalart and Leonard (1985), who devised an ingenious transformation that allows for the calculation of spatially evolving boundary layers in conjunction with periodic boundary conditions applied in the streamwise direction. While this method is elegant and highly accurate, it is more complicated than is necessary for the purpose of generating inflow data. A few key approximations are used in this work to arrive at a 'modified Spalart method' that is very easy to implement and efficient to use. The new method is shown to yield results that compare well with the computations of Spalart (1988). When used as a means of generating inflow data, the modified Spalart method is shown to be superior to existing approaches.

Lund, T. S.↗
NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗
DOE OSTI2023

A methodology to generate crystal-based molecular structures for atomistic simulations

Abstract We propose a systematic method to construct crystal-based molecular structures often needed as input for computational chemistry studies. These structures include crystal ‘slabs’ with periodic boundary conditions (PBCs) and non-periodic solids such as Wulff structures. We also introduce a method to build crystal slabs with orthogonal PBC vectors. These methods are integrated into our code, Los Alamos Crystal Cut ( LCC ), which is open source and thus fully available to the community. Examples showing the use of these methods are given throughout the manuscript.

42 ENGINEERING↗
DOE OSTI2020

Coordinate transformation methodology for simulating quasistatic elastoplastic solids

Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypo-elastoplastic mechanical model, and develop a projection method to enforce quasi-static equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1986

Simulation of the turbulent Rayleigh-Benard problem using a spectral/finite difference technique

The three-dimensional, incompressible Navier-Stokes and energy equations with the Bousinesq assumption have been directly simulated at a Rayleigh number of 3.8 x 10 to the 5th power and a Prandtl number of 0.76. In the vertical direction, wall boundaries were used and in the horizontal, periodic boundary conditions were used. A spectral/finite difference numerical method was used to simulate the flow. The flow at these conditions is turbulent and a sufficiently fine mesh was used to capture all relevant flow scales. The results of the simulation are compared to experimental data to justify the conclusion that the small scale motion is adequately resolved.

Eidson, T. M.↗
NASA NTRS2014

High Fidelity CFD Analysis and Validation of Rotorcraft Gearbox Aerodynamics Under Operational and Oil-Out Conditions

This document represents the evolving formal documentation of the NPHASE-PSU computer code. Version 3.15 is being delivered along with the software to NASA in 2013.Significant upgrades to the NPHASE-PSU have been made since the first delivery of draft documentation to DARPA and USNRC in 2006. These include a much lighter, faster and memory efficient face based front end, support for arbitrary polyhedra in front end, flow-solver and back-end, a generalized homogeneous multiphase capability, and several two-fluid modelling and algorithmic elements. Specific capability installed for the NASA Gearbox Windage Aerodynamics NRA are included in this version: Hybrid Immersed Overset Boundary Method (HOIBM) [Noack et. al (2009)] Periodic boundary conditions for multiple frames of reference, Fully generalized immersed boundary method, Fully generalized conjugate heat transfer, Droplet deposition, bouncing, splashing models, and, Film transport and breakup.

Gears↗
DOE OSTI2023

A Formulation of the Many-Body Expansion (MBE) for Periodic Systems: Application to Several Ice Phases

A new formulation of the many-body expansion (MBE) for periodic systems, based on their inherent translational symmetry, is introduced and applied to 7 ice polymorphs. This new formulation is built via a hierarchical procedure connecting gas phase unit cells over finite supercells to infinite solids. For finite supercells, it is demonstrated that this method successfully recovers the energetics while reducing the scaling of the calculation of the many-body terms by a factor of ~N, where N is the system size. Furthermore, the proposed framework delineates a straightforward way to obtain properties of macroscopic systems in the limit of an infinite cell. For periodic systems, the success of this approach is demonstrated by showing that the lattice energies computed (up to the 4-th order in the MBE) reproduce the lattice energies obtained using periodic boundary conditions with an Ewald summation for 7 polymorphs of ice (Ih, II, VIII, IX, XIII, XIV, XV). This development makes it possible to quantify, for the first time, the many-body contributions to the lattice energy of various ice polymorphs. The many-body (three-body and higher) interactions were found to vary significantly among the 7 ice phases, amounting between 7-24% of the total lattice energies. So, this development opens the door for obtaining insights into solid-state properties, while leveraging the computational benefits of the MBE.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗