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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Numerical similarity solution for a variable coefficient K(m, n) equation

A technique for finding numerical similarity solutions to an initial boundary value problem (IBVP) for generalized K(m, n) equations is described. The equation under consideration is nonlinear and has variable coefficients. The original problem is transformed with the aid of Lie symmetries to an initial value problem (IVP) for a nonlinear third-order ordinary differential equation. The existence and uniqueness of the solution are examined, and the problem is consequently solved with the aid of a finite-difference scheme for various values of the governing parameters. In lieu of an exact symbolic solution, the scheme is validated by comparing the numerical solutions with the approximate analytic solutions obtained with the aid of the method of successive approximations in their region of validity. The accuracy, efficiency, and consistency of the scheme are demonstrated. Numerical solutions to the original initial boundary value problem are constructed for selected parameter values with the aid of the transforms. The qualitative behavior of the solutions as a function of the governing parameters is analyzed, and it is found that the examined IBVPs for generalized K(m, n) equations with variable coefficients that are functions of time, do not admit solitary wave or compacton solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Simulating coupled surface–subsurface flows with ParFlow v3.5.0: capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model

Surface flow and subsurface flow constitute a naturally linked hydrologic continuum that has not traditionally been simulated in an integrated fashion. Recognizing the interactions between these systems has encouraged the development of integrated hydrologic models (IHMs) capable of treating surface and subsurface systems as a single integrated resource. IHMs are dynamically evolving with improvements in technology, and the extent of their current capabilities are often only known to the developers and not general users. This article provides an overview of the core functionality, capability, applications, and ongoing development of one open-source IHM, ParFlow. ParFlow is a parallel, integrated, hydrologic model that simulates surface and subsurface flows. ParFlow solves the Richards equation for three-dimensional variably saturated groundwater flow and the two-dimensional kinematic wave approximation of the shallow water equations for overland flow. The model employs a conservative centered finite-difference scheme and a conservative finite-volume method for subsurface flow and transport, respectively. ParFlow uses multigrid-preconditioned Krylov and Newton–Krylov methods to solve the linear and nonlinear systems within each time step of the flow simulations. The code has demonstrated very efficient parallel solution capabilities. ParFlow has been coupled to geochemical reaction, land surface (e.g., the Common Land Model), and atmospheric models to study the interactions among the subsurface, land surface, and atmosphere systems across different spatial scales. This overview focuses on the current capabilities of the code, the core simulation engine, and the primary couplings of the subsurface model to other codes, taking a high-level perspective.

58 GEOSCIENCES↗
DOE OSTI2023

Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization

Here, we consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of stochastic function evaluations within a common random number framework. We develop modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the stochastic approximations and provide global convergence results to the neighborhood of a locally optimal solution. We present numerical experiments on simulation optimization problems to illustrate the performance of the proposed algorithm. When compared with classical zeroth-order stochastic gradient methods, we observe that our strategies of adapting the sample sizes significantly improve performance in terms of the number of stochastic function evaluations required.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Assessing mass balance-based inverse modeling methods via a pseudo-observation test to constrain NO x emissions over South Korea

This study constrains NO x emissions by utilizing mass balance–based inverse modeling methods and examines the optimization of inverse modeling conditions through a pseudo-observation test for South Korea, which has complex topography. Here, we applied mass balance–based inverse modeling methods such as Basic Mass Balance (BMB), Finite Difference Mass Balance (FDMB), and Iterative Finite Difference Mass Balance (IFDMB). We performed a numerical simulation of air quality using the Community Multi-scale Air Quality (CMAQ) model to calculate the NO 2 column density required for the inverse modeling. The pseudo-observation test was performed according to season, modeling resolution, and regridding methodology of satellite observation data to identify various conditions while applying the inverse modeling for South Korea. Comparing the inverse modeling results from the BMB, FDMB, and IFDMB methods, IFDMB was the most effective method in constraining NO x emissions in the South Korean region since it minimized smearing effects (i.e., transport-induced errors) through iterative calculations. The accuracy of the constrained NO x emissions using mass balance–based inversions in South Korea was the highest in the summer due to the minimized smearing effects, and the 9 km resolution modeling was the most efficient for inverse modeling of the region. In addition, the results of inverse modeling varied depending on the regridding methods, implying the importance of using a suitable regridding method and modeling resolution. This study used pseudo-observations, but the inversions are expected to be applied based on actual satellite data in the future.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Modeling and analysis of mixed convection stagnation point flow of nanofluid towards a stretching surface: OHAM and FEM approach

A theoretical study of mixed convection stagnation point flow towards a stretching surface is presented. The governing boundary layer equations are transformed into a set of highly nonlinear ordinary differential equations using suitable similarity transforms. The semi-analytical solution is obtained using optimal homotopy analysis method (OHAM) and the numerical solution is obtained via finite element method (FEM). Solutions obtained via two different approaches are in excellent agreement, which validates the accuracy of present analysis. In a special case, the present OHAM solution is also validated with the earlier available results. Effect of pertinent flow parameters on the skin friction coefficient and Nusselt number is presented in tabular form, whereas the velocity, temperature and nanoparticle distribution are presented in graphical forms. Further, a quadratic multiple regression analysis on numeric data of skin friction coefficient and Nusselt number is performed. The findings suggest that velocity slip assists the fluid motion in presence of buoyancy forces, whereas it exhibits a retarding nature on fluid motion when no buoyancy forces exist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. II. Implicit Methods

We consider specific realizations of different implicit generalized Runge–Kutta methods as applied to the numerical integration with respect to time of initial-boundary-value problems for the second-order parabolic equations and investigate their spectral stability. It is shown that all implicit generalized Runge–Kutta methods are unconditionally spectrally stable but some of them have the conditional property of monotonicity of the numerical solution with respect to time. The functions of spectral stability of the implicit generalized Runge–Kutta methods are rational. We compare the analytic solution of the nonstationary one-dimensional problem of heat conduction with the numerical solutions of this problem obtained by different implicit generalized Runge–Kutta methods. It is shown that, in this case, the application of the one-stage Radau methods with subsequent discretization of the problem with respect to the space variable leads to the classical forward finite difference scheme (Laasonen scheme), whereas the use of the one-stage Gauss–Legendre method leads to a six-point symmetric scheme (Crank–Nicolson scheme). It is shown that diagonally implicit generalized Nørsett and Burrage methods are realized in almost the same way as the one-stage Radau and Gauss–Legendre methods but their accuracy in the time step is 10–1000 times higher. On the basis of comparison of the numerical and analytic solutions, we conclude that, in order to get practically suitable numerical solutions without any restrictions on the time step, it is reasonable to use one- and three-stage generalized Radau methods or two- and four-stage Lobatto IIIC methods. All other explicit and implicit generalized Runge–Kutta methods require certain restrictions imposed on the time step.

42 ENGINEERING↗
DOE OSTI2018

Two-step perfectly matched layer for arbitrary-order pseudo-spectral analytical time-domain methods

Numerical simulation of an electrodynamic system in empty space requires the implementation of open boundary conditions (BC) to terminate the solution of Maxwell’s equations on the boundaries of the computational domain. The Perfectly Matched Layer (PML) has become the method of choice for open BC with wave equations, as it is straightforward and relatively easy to implement, and offers very efficient and user-adjustable absorption rates. PMLs are most often employed with the Finite-Difference Time-Domain (FDTD) algorithm, which in its most common implementation offers second-order accuracy in space and time on Cartesian grids. Yet, simulations (including some class of electromagnetic Particle-In-Cell simulations) that require higher precision may resort to higher-order Maxwell solvers employing extended finite-difference stencils, or even to pseudo-spectral Maxwell solvers, for which a general, versatile and efficient formulation of the PML has been missing so far. Here we propose a novel “two-step” formulation of the PML that is simple, very versatile and can be used as is with any Maxwell solver. In particular, it is applicable to a large class of Maxwell solvers including the arbitrary-order Pseudo-Spectral Analytical Time-Domain (PSATD) solver, which offers arbitrarily low numerical dispersion when increasing solver order and becomes dispersion-free at infinite order. Analysis and numerical simulations demonstrate that the new formulation is as efficient as the standard PML formulation, both for the FDTD and the PSATD implementations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A multigrid waveform relaxation method for solving the poroelasticity equations

In this work, a multigrid waveform relaxation method is proposed for solving a collocated finite difference discretization of the linear Biot’s model. This gives rise to the first space–time multigrid solver for poroelasticity equations in the literature. The waveform relaxation iteration is based on a point-wise Vanka smoother that couples the pressure variable at a grid-point with the displacements around it. A semi-algebraic mode analysis is proposed to theoretically analyze the convergence of the multigrid waveform relaxation algorithm. This analysis is novel since it combines the semi-algebraic analysis, suitable for parabolic problems, with the non-standard analysis for overlapping smoothers. The practical utility of the method is illustrated through several numerical experiments in one and two dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Numerical Simulation of M9 Megathrust Earthquakes in the Cascadia Subduction Zone

We estimate ground motions in the Pacific Northwest urban areas during M9 subduction scenario earthquakes on the Cascadia megathrust by simulating wave propagation from an ensemble of kinematic source descriptions. Velocities and densities in our computational mesh are defined by integrating the regional Cascadia Community Velocity Model (CVM) v1.6 (Stephenson et al. P-and S-wave velocity models incorporating the Cascadia subduction zone for 3D earthquake ground motion simulations—update for open-file report 2007–1348, US Geological Survey, 2017) including the ocean water layer with a local velocity model of the Georgia basin (Molnar, Predicting earthquake ground shaking due to 1D soil layering and 3D basin structure in SW British Columbia, Canada, 2011), including additional near-surface velocity information. We generate six source realizations, each consisting of a background slip distribution with correlation lengths, rise times and rupture velocities consistent with data from previous megathrust earthquakes (e.g., 2011 M 9 Tohoku or 2010 M 8.8 Maule). We then superimpose M ~ 8 subevents, characterized by short rise times and high stress drops on the background slip model to mimic high-frequency strong ground motion generation areas in the deeper portion of the rupture (Frankel, Bull Seismol Soc Am 107(1):372–386, 2017). The wave propagation is simulated using the discontinuous mesh (DM) version of the AWP finite difference code. We simulate frequencies up to 1.25 Hz, using a spatial discretization of 100 m in the fine grid, resulting in surface grid dimensions of 6540 × 10,728 mesh points. At depths below 8 km, the grid step increases to 300 m. We obtain stable and accurate results for the DM method throughout the simulation time of 7.5 min as verified against a solution obtained with a uniform 100 m grid spacing. Peak ground velocities (PGVs) range between 0.57 and 1.0 m/s in downtown Seattle and between 0.25 and 0.54 m/s in downtown Vancouver, while spectral accelerations at 2 s range between 1.7 and 3.6 m/s 2 and 1.0 and 1.3 m/s 2 , respectively. These long-period ground motions are not significantly reduced if plastic Drucker-Prager yielding in shallow cohesionless sediments is taken into account. Effects of rupture directivity are significant at periods of ~ 10 s, but almost absent at shorter periods. We find that increasing the depth extent of the subducting slab from the truncation at 60 km in the Cascadia CVM version 1.6 to ~ 100 km increases the PGVs by 15% in Seattle and by 40% in Vancouver.

finite difference method↗
DOE OSTI2025

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗
DOE OSTI2017

Numerical methods for the inverse problem of density functional theory

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic model systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Investigation of resonant mode sensitivity in PhC based ring resonators

Quality factor and refractive index sensitivity are significant parameters in designing optical devices based on ring resonators such as filters, demultiplexers, switches in which the ring resonator is considered as an elementary componant. In this paper, we propose a photonic crystal ring resonator with super-ellipse shaped core. The proposed ring resonator placed between two parallels waveguides (bus waveguide and drop waveguide). The transmission efficiency of the proposed ring resonator at λ = 1547.3 nm is about 95% with bandwidth and quality factor values equal to 0.7 nm and 2210, respectively. Simulation results show that the resonance sensitivity upon refractive index variation of coupling, outer layer, adjacent and scattering rods are Δλ/Δn = 0.2 nm/0.01, Δλ/Δn = 0.225 nm/0.01, Δλ/Δn = 0.125 nm/0.01 and Δλ/Δn = 0.05 nm/0.01, respectively. The finite different time domain and plane wave expansion methods are used to calculate the outputs spectrum and band gap, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Slow light enhanced bio sensing properties of silicon sensors

In this paper, we investigated slow light to increase sensitivity and quality factor of our recently designed bio-sensors. A finite difference time domain and Plane Wave Expansion methods are employed to figure out sensors’ performances. We proposed slow light based photonic crystal structures with elliptical cells and we obtained higher sensitivity and quality factor as previously reported. For the first proposed sensor, the results showed that quality factor increased from 570 to 723 and a detection limit below 10{sup −3}. For the second sensor, the sensitivity increased from 550 to 650 nm/RIU and the detection limit is around 10{sup −3}. These two proposed structures would offer great potential for novel compact biosensors in medical application.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Investigation of Various Transformer Topologies for HF Isolation Applications

High-frequency (HF) transformers are an essential part of many power electronic devices. The performance and behavior of HF transformers can greatly affect the efficiency and performance of all systems, particularly, from a parasitic parameter point of view. In this article, HF transformers' parasitic parameters, such as leakage inductances and parasitic capacitances, are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements of different structures and winding arrangements. Also, the magnetic field, electric field, electric displacement field, and electric potential distribution within the transformers are simulated and analyzed. Four different HF transformers with E and U cores with different windings are designed and analyzed. Investigation outcomes help to classify structures according to the trade-off between leakage inductances and series parasitic capacitances. This information can later be used for the optimal selection and design of transformers as a function of their operating frequency for any power rating and voltage level. Moreover, 3-D FEM and experimental results validate the proposed methodology to be used for designing HF transformers in high-voltage/power applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Level-set Modeling Simulations of Chemical Vapor Infiltration for Ceramic Matrix Composites Manufacturing

Silicon-carbide (SiC) reinforced ceramic matrix composites (CMCs) are a key enabling technology to reduce fuel consumption and emissions of gas turbine engines. In one manufacturing approach, chemical vapor infiltration (CVI) is limited to only coating SiC fibers. The preform is then fabricated using a lay-up of basic plys or 2-D woven sheets composed of the precoated fibers. At the other extreme, CVI is used to completely densify a 3-D woven preform shaped almost like the gas turbine component itself. The latter approach is more suitable for highly engineered components which sit directly in the gas path of the engine, for example, a high pressure turbine blade. In this case, the geometry is necessarily complex for aerodynamic, stress, and lifing (multi-physics) requirements. Presently, optimizing the CVI-dominated manufacturing approach is largely by trial-and-error. In this work, a first-principles modeling of CVI is performed to realize optimization of SiC/SiC CMC manufacturing. The modeling is based on a level-set framework to describe the interface between the vapor and solid phases. A finite-difference numerical scheme using an immersed boundary method is developed for fixed, structured meshes. Massively parallel direct numerical simulations (DNS) of CVI through fiber-woven geometries are performed using one-step chemistry, and over a range of Thiele moduli. Illustrative applications of the resulting large DNS data sets are given, including the development of fiber-weave specific infiltration models and structure functions for mean-field (porous media) Computational Fluid Dynamics (CFD) simulations of CVI.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Improvements to the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nonoverlapping block smoothers for the Stokes equations

Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development and analysis of new block smoothers for the Stokes equations that are discretized on staggered grids. These smoothers are nonoverlapping and therefore desirable due to reduced computational costs. Traditional geometric multigrid methods are based on simple pointwise smoothers. However, using multigrid methods to efficiently solve more difficult problems such as the Stokes equations leads to computationally more expensive smoothers, for example, overlapping block smoothers. Nonoverlapping smoothers are less expensive, but have been considered less efficient in the literature. In this paper, we develop new nonoverlapping smoothers, the so-called triad-wise smoothers, and show their efficiency within multigrid methods to solve the Stokes equations. In addition, we compare overlapping and nonoverlapping smoothers by measuring their computational costs and analyzing their behavior by the use of local Fourier analysis.

97 MATHEMATICS AND COMPUTING↗