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

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

PLATO (Parallel Load Assignment Tool): A Parallel Workload Partitioner for Particle-based Methods

A key first step in many large-scale high-performance scientific computing applications is the distribution of the computational domain across all participating processors of a parallel computing platform such as a shared memory machine, cluster or a tightly-coupled supercomputer. The primary goal of such a partitioning step is to ensure that the computational work performed by each process remains load-balanced throughout the execution of the parallel application. In this project, a general-purpose parallel partitioning tool, code-named PLATO, was designed and implemented. PLATO assumes that the workload is a set of points in an n-dimensional metric space. These points are abstractions of computational units that may represent point-like computational units such as celestial objects in astrophysics, atoms in materials sciences and molecules in biology/chemistry, or may represent more abstract computational units such as grid points in finite difference methods, grid elements in finite element methods or n-dimensional points in the feature space of a host of other applications. PLATO supports several key and useful capabilities, namely: (a) multiple load partitioning strategies, (b) support for arbitrary user-defined processor topology, (c) pre-fetching data from neighboring processors based on user-defined parameters, and (d) support for arbitrary number and types of attributes associated with each point in the computational domain. PLATO is implemented in the C programming language using Message Passing Interface (MPI) for inter-processor communications and its parallel performance tested on up to 48 processors of a shared memory machine. This report includes a detailed performance study of PLATO using parallel speedup and iso-efficiency as the two main metrics of parallel performance. In addition, a user manual and DOXYGEN generated code documentation have been included for completeness.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials

In this report we compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at $O(1/\varepsilon)$. In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size $h$ and time step $\tau$ as well as the small parameter $\varepsilon$. Based on the results, in order to obtain "correct" numerical solutions up to the time at $O(1/\varepsilon)$, the $\varepsilon$-scalability (or meshing strategy requirement) of the FDTD methods should be taken as $h = O(\varepsilon^{1/2})$ and $\tau = O(\varepsilon^{1/2})$. To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Quantum Spectral Methods for Differential Equations

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ϵ with complexity poly(log(1/ϵ)), no such algorithm was previously known for differential equations with time-dependent coefficients. In this work, we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd, log(1/ϵ)).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Interface learning in fluid dynamics: Statistical inference of closures within micro–macro-coupling models

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.

42 ENGINEERING↗
DOE OSTI2017

Mathematical Simulation of the Migration of Radionuclides in a Soil Medium Under Nonisothermal Conditions with Account for Catalytic Microparticles and Nonlinear Processes

The problem of mathematical simulation of the vertical migration of radionuclides in a catalytic porous medium under nonisothermal conditions is considered. A numerical solution of the corresponding one-dimensional nonlinear boundary-value problem is obtained by the finite difference method. Numerical experiments are carried out and their analysis is made.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

A higher order approximate static condensation method for multi-material diffusion problems

The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or moment-of-fluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P 1 (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Calculation of Energy States of Excitons in Square Quantum Wells

The ground and excited energy states of excitons in single square GaAs-based quantum wells are found by the numerical solution of the three-dimensional Schrödinger equation. This equation is obtained within the envelope-function formalism from the exciton energy operator using the spherical approximation of the Luttinger Hamiltonian. Precise results for the exciton states are achieved by the finite-difference method. The radiative decay rates of the calculated states are also determined.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Orbital Advection with Magnetohydrodynamics and Vector Potential

Orbital advection is a significant bottleneck in disk simulations, and a particularly tricky one when used in connection with magnetohydrodynamics. We have developed an orbital advection algorithm suitable for the induction equation with magnetic potential. The electromotive force is split into advection and shear terms, and we find that we do not need an advective gauge since solving the orbital advection implicitly precludes the shear term from canceling the advection term. We prove and demonstrate the third order in time accuracy of the scheme. The algorithm is also suited to non-magnetic problems. Benchmarked results of (hydrodynamical) planet–disk interaction and of the magnetorotational instability are reproduced. We include detailed descriptions of the construction and selection of stabilizing dissipations (or high-frequency filters) needed to generate practical results. The scheme is self-consistent, accurate, and elegant in its simplicity, making it particularly efficient for straightforward finite-difference methods. As a result of the work, the algorithm is incorporated in the public version of the Pencil Code, where it can be used by the community.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Numerical Modeling of Ultra Wideband Combined Antennas

With the help of a program we developed, based on the finite difference method in the time domain, we have investigated the characteristics of ultra wideband combined antennas in detail. The antennas were developed to radiate bipolar pulses with durations in the range 0.5–3 ns. Data obtained by numerical modeling are compared with the data of experimental studies on antennas and have been used in the synthesis of electromagnetic pulses with maximum field strength.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The Interface Influence in TiN/SiN{sub x} Multilayer Nanocomposite Under Irradiation

The paper focuses on studying the kinetics of radiation-induced point defects formed in TiN/SiN{sub x} multilayer nanocomposites with account of their generation, diffusion recombination, and the influence of sinks functioning as interfaces. In order to describe the kinetics in nanocrystalline TiN and amorphous SiN{sub x} phases, a finite-difference method is used to solve the system of balance kinetic equations for absolute defect concentrations depending on the spatiotemporal variables. A model of the disclination-dislocation interface structure is used to study the absorption of radiation-induced point defects on the boundaries in created stress fields. It is shown that the interface effectively absorbs point defects in these phases of TiN/SiN{sub x} multilayer nanocomposite, thereby reducing their amount within the space between phases. This behavior of point defects partially explains a mechanism of the radiation resistance in this type of nanocomposites.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2019

Miniband formation engineering in GaN/AlN superlattices with constant total effective length

In this work, we study the miniband formation procedure in GaN/AlN constant total effective length superlattices by means of the subband energy calculations. We calculate the transmission coefficients and miniband structures of the systems by means of the transfer matrix and finite difference methods, respectively. The miniband structures obtained by using these methods confirm each other. Here, we observe a nonlinear miniband gap behavior as the number of wells changes. Now, we can tune the width of each miniband and minigap by means of the number of wells and the total effective length of the system. By using the strategy of fixing the total length of the system and optimizing the number of layers inside it, we can find the same miniband widths as the usual superlattice (fixing the well width, not the total system length). However, in the earlier case (our proposal), fabrication of the device may need fewer amounts of the material and may lead to smaller device sizes, because we fixed the total system length.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

We present a semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose spatial discretization yields a tridiagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor semi-analytic solutions are available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Extreme sensitivity of higher-order interatomic force constants and thermal conductivity to the energy surface roughness of exchange-correlation functionals

In this Letter, we report that the fourth-order interatomic force constants (4th-IFCs) are significantly sensitive to the energy surface roughness of exchange-correlation (XC) functionals in density functional theory calculations. This sensitivity, which is insignificant for the second- (2nd-) and third-order (3rd-) IFCs, varies for different functionals in different materials and can cause misprediction of thermal conductivity by several times of magnitude. As a result, when calculating the 4th-IFCs using the finite difference method, the atomic displacement needs to be taken large enough to overcome the energy surface roughness, in order to accurately predict phonon lifetime and thermal conductivity. We demonstrate this phenomenon on a benchmark material (Si), a high-thermal conductivity material (BAs), and a low thermal conductivity material (NaCl). For Si, we find that the LDA, PBE, and PBEsol XC functionals are all smooth to the 2nd- and 3rd-IFCs but all rough to the 4th-IFCs. This roughness can lead to a prediction of nearly one order of magnitude lower thermal conductivity. For BAs, all three functionals are smooth to the 2nd- and 3rd-IFCs, and only the PBEsol XC functional is rough for the 4th-IFCs, which leads to a 40% underestimation of thermal conductivity. For NaCl, all functionals are smooth to the 2nd- and 3rd-IFCs but rough to the 4th-IFCs, leading to a 70% underprediction of thermal conductivity at room temperature. In conclusion, with these observations, we provide general guidance on the calculation of 4th-IFCs for an accurate thermal conductivity prediction.

42 ENGINEERING↗
DOE OSTI2018

Numerical investigation on two-fluid model (micropolar-Newtonian) for pulsatile flow of blood in a tapered arterial stenosis with radially variable magnetic field and core fluid viscosity

In the present study, an unsteady two-fluid model of blood through a tapered arterial stenosis with variable viscosity in the presence of variable magnetic field has been investigated. In this model, blood in the core region is assumed to be micropolar and plasma in the peripheral layer as Newtonian. Finite difference method is employed in solving the governing equations. The solutions for velocity, flow rate, wall shear stress and flow resistance are computed numerically. A comparison between the velocity profiles obtained by the present study and the experimental data is made and a good agreement between them is found. The model is used to study the effect of parameters such as taper angle, radially variable viscosity, hematocrit, the coupling number, the micropolar parameter, magnetic field and plasma layer thickness on physiologically important parameters such as wall shear stress distribution in the stenotic region and flow resistance. The results in the case of constant magnetic field and variable magnetic field are compared to study the effects of magnetic field on the flow of blood. It is found that the magnitudes of wall shear stress and flow resistance are higher in the case of variable magnetic field. It is important to note that the flow resistance is higher for magneto-micropolar fluid than the micropolar fluid. The wall shear stress decreases with increasing hematocrit parameter whereas flow resistance increases with hematocrit when the applied pressure gradient is held fixed. The model clearly shows the situation of a patient with a tapered arterial stenosis under feverish condition. Due care has been taken to compare the present theoretical results with the existing ones including experimental results and good agreement between them has been observed both qualitatively and quantitatively.

42 ENGINEERING↗
DOE OSTI2018

Semi-analytical sensitivity analysis for nonlinear transient problems

Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; however, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

42 ENGINEERING↗
DOE OSTI2019

Real time time-dependent density functional theory using higher order finite-element methods

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real time using higher order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this end, we develop an a priori mesh adaption technique, based on the semidiscrete (discrete in space but continuous in time) error estimate on the time-dependent Kohn-Sham orbitals, to construct an efficient finite-element discretization. Subsequently, we obtain the full-discrete error estimate to guide our choice of the time step. We employ spectral finite elements along with special reduced order quadrature to render the overlap matrix diagonal, thereby simplifying the inversion of the overlap matrix that features in the evaluation of the discrete time-evolution operator. We use the second-order Magnus operator as the time-evolution operator, wherein the action of the discrete Magnus operator, expressed as exponential of a matrix, on the Kohn-Sham orbitals is obtained efficiently through an adaptive Lanczos iteration. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization, for both pseudopotential and all-electron calculations. We demonstrate a staggering 100-fold reduction in the computational time afforded by higher order finite elements over linear finite elements, for both pseudopotential and all-electron calculations. Further, for similar level of accuracy, we obtain significant computational savings by our approach as compared to state-of-the-art finite-difference methods. Here, we also demonstrate the competence of higher order finite elements for all-electron benchmark systems. Lastly, we observe good parallel scalability of the proposed method on many hundreds of processors.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Exploring the impact of surface topography on Rayleigh-Bénard dry convection in the Pi cloud chamber using OpenFOAM: In cylindrical and rectangular geometries

The Pi convection-cloud chamber can generate steady-state turbulence in both rectangular and cylindrical shapes via Rayleigh-Bénard convection (RBC) by maintaining warm bottom and cold top surfaces. Although most experiments in the Pi chamber were conducted in cylindrical shapes, all previous Pi chamber simulations were conducted in a rectangular shape due to the limitations of those models to discretize a cylindrical domain when using the finite difference method therein. Here, we use OpenFOAM, an open-source finite-volume-based Computational Fluid Dynamics (CFD) software package, to conduct Large-Eddy Simulation (LES) of dry RBC in the Pi chamber at high Rayleigh numbers (10 8 to 10 9 ). Results show that large-scale circulation (LSC) direction varies in the chamber with a constant side wall temperature. Imposing a slight temperature imbalance at the side wall ranging from 0.1 to 0.7 degrees can lock the LSC, aligning better with Pi chamber observations, particularly at higher Rayleigh numbers. In addition, we examine the impact of surface topography on LSC and heat transfer in RBC systems within cylindrical and rectangular shapes under varying conditions. Results show that roughing top/bottom surfaces by adding bars of a few tens millimeters height can strengthen thermal plumes and enhance temperature fluctuations in the chamber. Furthermore, we observe that different bar height configurations lead to notable changes in LSC orientation and thermal stratification, highlighting the complex interactions between surface features and convection patterns. This finding highlights how surface topography and chamber geometry affect Rayleigh-Bénard convection, improving understanding of turbulent heat transfer and atmospheric boundary-layer processes. Direct Numerical Simulations (DNS) are also conducted to validate LES results. In conclusion, while LES effectively captures qualitative behaviors seen in DNS, it tends to underestimate velocity variances near walls, illustrating a trade-off between computational efficiency and accuracy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗