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DOE OSTI2019

Method for Measuring Dry Density of Compacted Bentonite Mixture Soil Using 3D Laser Scanner data - 19119

The bentonite mixture soil is planned to be used for the low-permeability layer of low-level radioactive waste (LLW) disposal facilities. The construction of the bentonite mixture soil is similar to that of normal soil construction, and the rolling pressure and/or vibration compaction are used. The quality control of construction is the same as normal soil work, and the construction management has to confirm that the compaction degree (that is ratio of the dry density to the modified proctor curve) is above specified value. As a method of measuring the dry density after construction, the conventional methods are the core cutter method and the sand replacement method. The measurement principle of these methods is simple and the reliability of the measurement value is high, but during measurements digging holes disturb the construction place, and the measurement duration is a disadvantage in these methods. Therefore, we developed a non-destructive method that can make measurements in a short time. The developed method uses the correlation between the density change and the layer thickness change before and after compaction, and estimates the density after compaction from the height change obtained from the survey results. However, since the material is compressed while the cross-sectional area spreads, this cross-sectional area change is also taken into consideration. By using the point cloud data of the 3D laser scanner surveying, it is possible to obtain almost continuous data in a short period of time. Corrected dry density values calculated by the above procedure ρ'{sub 3D} are generally consistent with dry density after compaction ρ{sub core} by the core cutter method. This method differs depending on the boundary conditions of the bottom and the side of the construction place. Then, the reliability of the method was evaluated by applying it to two boundary conditions and comparing it with the core cutter method. The proposed estimation method showed good agreement with the core cutter method. Therefore, it was confirmed that it is possible to estimate dry density with high reliability. Although this method needs to be used in set with core cutter method, the measurement frequency of the core cutter method can be reduced, and the measurement of a vast area can be done in a short time without disturbance. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

The multigrid preconditioned conjugate gradient method

A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.

Tatebe, Osamu↗

DOE OSTI2019

Open-air Demolition: Validation of EPA Approved Alternative Method for Emission Estimation - 19397

Emissions from open-air demolition of US Department of Energy (DOE) facilities are regulated by the US Environmental Protection Agency (EPA) under 40 CFR 61 subpart H. This regulation requires that facilities estimate emissions using an EPA approved method from activities such as open-air demolition prior to commencing the activity. Should those emissions exceed certain thresholds, the facility may be required to obtain an Approval to Construct or Modify the facility and/or installed monitoring methods meeting methods acceptable to EPA. There are no EPA approved methods that are specific to open-air demolition methods. For this project the DOE and CH2M Hill BWXT elected to prepare an alternative method specific to open-air demolition. EPA conditionally approved the method but required validation of the method during the demolition of the Vitrification Facility at the West Valley Demonstration Project (WVDP) before use for open-air demolition at other WVDP structures. The validation method included detailed source characterization, close-in ambient samplers, and a comparison of measured results to predicted emissions using AERMOD (American Meteorological Society (AMS) and U.S. Environmental Protection Agency (EPA) Regulatory Model). The methods evaluated include hydraulic hammers, mechanical shears, load out of waste and handling of the debris piles. The validation method involved the collection and analysis of ambient air samples from air samplers located at strategic locations within the projected plume path of the demolition activities. The analytical results from the air samplers were then compared to ambient air concentrations predicted at the sampler locations with the EPA model AERMOD. The input to the AERMOD software is a source term developed weekly using the alternative method and material at risk disturbed during each week. To account for the building wake effects of the surrounding structures, virtual point sources were developed in the AERMOD model and placed at the locations of the demolition, debris piles, debris handling and load out areas. It was found that the factors used for hydraulic hammering were extremely conservative and that emissions from the debris pile were not only the primary emission source, but that the moisture content of the debris pile and the wind speed were critical factors that must be considered in future open-air demolition projects. Based on the results of the validation process, adjustments were made to the alternative method. The final validated alternative method provides an approach for estimating airborne emissions from open-air demolition methods and techniques. The method will be used in lieu of 40 CFR 61 Appendix D to estimate emissions from future open-air demolition projects at the WVDP. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

This paper presents improvement and performance evaluation of the “perturbation source method”, which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an “on-the-fly” technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section. - Highlights: • A Monte Carlo perturbation method known as “perturbation source method” is examined. • The method outperforms other perturbation methods when the perturbed region is small. • The efficiency depends on virtual scatterings added by a user-specified parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

The Parareal Method for Solving Space-Dependent Neutron Kinetics Equations in Hexagonal-z Geometry

Neutron kinetics plays an important role in reactor safety and analysis. The backward Euler method is the most widely used time integration method in the calculation of space-dependent nuclear reactor kinetics. Xia (2006) used this method to discretize the derivative of flux, and adopted the analytic integration to discretize the delayed neutron precursor concentrations. Diagonally Implicit Runge-Kutta (DIRK) method owns high accuracy and excellent stability, and it was applied in the rectangle core for calculating core the nuclear reactor kinetics by Wenbo Zhao (2013). Recently, DIRK was applied to the neutron kinetics for hexagonal-z geometry application (CAI, 2016). As solving the neutron kinetics equations is very time-consuming and the number of available cores continues to increase with parallel architectures evolving, parallel algorithms need to be designed in order to effectively utilize the available resources. However, it is difficult to parallel in time axis because the later moment is strongly dependent on the previous moment. Some methods have been proposed to parallel in time algorithm over the last decades. One of the famous methods to realize time parallelism is the Parareal algorithm (Lions, 2001), which offers a promising approach to increase the degree of concurrency. More than one decade from this method first proposed, this method has been studied and applied in the many fields of applied mathematics, physics, chemistry, parallel computing, etc. Fischer (2014 applied the Parareal method in the field of the Navier-Stokes Equations. Baudron (2014) combined the Parareal method with finite element method to solve the neutron kinetics equations, where the Parareal method was implemented based on the implicit Euler method or method. In this paper, the Parareal method is studied in the hexagonal-z geometry with the help of DIRK developed for neutron kinetics equations (CAI, 2016)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Recovery of DNA from fired and unfired cartridge casings: comparison of two DNA collection methods

For over 10 years, various studies have attempted to increase the recovery of DNA from ammunition by modifying the DNA collection, extraction, purification, and amplification procedures, with varying levels of success. This study focused on the “soaking” method of Montpetit & O’Donnell [1] and the “rinse-and-swab" method of Bille et al. [2]. First, testing for the presence of exogenous DNA, 210 boxed cartridges (brass, steel, and nickel-plated) from nine manufacturers were swabbed and DNA was extracted, concentrated, and quantified. Extracts that quantified > 0 ng/µL (44 of 210) were amplified and genotyped with GlobalFiler™. Of those, only one extract yielded two alleles indicating that the manufacturing and packaging of ammunition was virtually DNA free. Next, to obtain a baseline comparison of two DNA collection methods on a non-metallic substrate and identify a suitable number of cells to spot on cartridges, different DNA input amounts of primary human adult epidermal keratinocytes (HEKa) were tested. Thereafter, 300 brass and 300 nickel-plated, cartridges were spotted with HEKa cells containing ~5 ng of DNA, fired or unfired, and processed with either method. Finally, five methods representing hybrids of the soaking and rinse-and-swab methods were tested to determine if variations of those methods could be used to increase DNA yield and recovery. The results show that the soaking method consistently yielded more DNA than the rinse-and-swab method from a non-metallic substrate. However, the comparison study demonstrated that both methods performed comparably for cartridges. On average, the soaking method recovered 0.25 ng of DNA (5.1% recovery) and the rinse-and-swab method recovered 0.28 ng (5.8% recovery). However, average recoveries were significantly different among three analysts and considerable variation in yields were observed, possibly due to storage time. Furthermore, consistent with prior reports, the DNA recovered from brass casings was only 16% of that recovered from nickel-plated casings and the average yield of DNA from fired casings was reduced to 67% of unfired casings. Moreover, DNA extracts from brass or nickel-plated casings did not appear to contain amplification inhibitors and only 30/596 appeared severely degraded. Finally, both the published rinse-and-swab and soaking methods yielded more DNA than all modifications of the two methods. Overall, both methods yielded equivalent DNA quantities. Additionally, recovery of DNA from any given cartridge casing may be dependent on storage time as well as the skill, proficiency, and experience of the analyst and may reflect stochastic effects, particularly for casings containing low copy and/or degraded DNA.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Raju, I. S.↗

NASA NTRS1996

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Molenaar, J.↗

DOE OSTI2019

The Subray Method of Characteristics

The MPACT code is being jointly developed by the University of Michigan and Oak Ridge National Laboratory. It uses the 2-D/1-D method to solve neutron transport problems for reactors. The 2-D/1-D method decomposes the problem into a stack of 2-D planes and uses a high-fidelity transport method to resolve all heterogeneity in each plane. These planes are then coupled axially, using a lower-order solver. With this scheme, three-dimensional (3-D) solutions to the transport equation can be obtained at a much lower cost. The 2-D/1-D method assumes that the materials are axially homogeneous for each 2-D plane. Violation of this assumption requires homogenization, which can significantly reduce the accuracy of the calculation. This work proposes the subray method of characteristics (subray MOC) as a solution to this problem. Subray MOC is a subgrid method that allows local heterogeneities to be directly resolved by method of characteristics while treating the rest of the 2-D plane as axially uniform. This improves the accuracy in the neighborhood of the heterogeneity while minimizing the increase in run time. The method was applied to variations of the C5G7 benchmark problems and compared with a previously developed subgrid method called the subplane collision probabilities (SCP) method. Comparisons were made among results obtained using subray MOC, the SCP method, and no subgrid method. Subray MOC consistently performed best, reducing maximum 3-D power distribution errors from as high as 30% to 2% or less. Moreover, it consistently outperformed the SCP method with run times that were shorter than the reference calculations.

2-D/1-D method↗

DOE OSTI2017

Effect of preparation methods on dispersion stability and electrochemical performance of graphene sheets

Chemical exfoliation is one of the most important strategies for preparing graphene. The aggregation of graphene sheets severely prevents graphene from exhibiting excellent properties. However, there are no attempts to investigate the effect of preparation methods on the dispersity of graphene sheets. In this study, three chemical exfoliation methods, including Hummers method, modified Hummers method, and improved method, were used to prepare graphene sheets. The influence of preparation methods on the structure, dispersion stability in organic solvents, and electrochemical properties of graphene sheets were investigated. Fourier transform infrared microscopy, Raman spectra, transmission electron microscopy, and UV–vis spectrophotometry were employed to analyze the structure of the as-prepared graphene sheets. The results showed that graphene prepared by improved method exhibits excellent dispersity and stability in organic solvents without any additional stabilizer or modifier, which is attributed to the completely exfoliation and regular structure. Moreover, cyclic voltammetric and electrochemical impedance spectroscopy measurements showed that graphene prepared by improved method exhibits superior electrochemical properties than that prepared by the other two methods. - Graphical abstract: Graphene oxides with different oxidation degree were obtained via three methods, and then graphene with different crystal structures were created by chemical reduction of exfoliated graphene oxides. - Highlights: • Graphene oxides with different oxidation degree were obtained via three oxidation methods. • The influence of oxidation methods on microstructure of graphene was investigated. • The effect of oxidation methods on dispersion stability of graphene was investigated. • The effect of oxidation methods on electrochemical properties of graphene was discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Downwinding for preserving strong stability in explicit integrating factor Runge-Kutta methods

Here strong stability preserving (SSP) Runge-Kutta methods are desirable when evolving in time problems that have discontinuities or sharp gradients and require nonlinear non-inner-product stability properties to be satisfied. Unlike the case for L 2 linear stability, implicit methods do not significantly alleviate the time-step restriction when the SSP property is needed. For this reason, when handling problems with a linear component that is stiff and a nonlinear component that is not, SSP integrating factor Runge-Kutta methods may offer an attractive alternative to traditional time-stepping methods. The strong stability properties of integrating factor Runge-Kutta methods where the transformed problem is evolved with an explicit SSP Runge-Kutta method with non-decreasing abscissas was recently established. However, these methods typically have smaller SSP coefficients (and therefore a smaller allowable time-step) than the optimal SSP Runge-Kutta methods, which often have some decreasing abscissas. In this work, we consider the use of downwinded spatial operators to preserve the strong stability properties of integrating factor Runge-Kutta methods where the Runge-Kutta method has some decreasing abscissas. We present the SSP theory for this approach and present numerical evidence to show that such an approach is feasible and performs as expected. However, we also show that in some cases the integrating factor approach with explicit SSP Runge-Kutta methods with non-decreasing abscissas performs nearly as well, if not better, than with explicit SSP Runge-Kutta methods with downwinding. In conclusion, while the downwinding approach can be rigorously shown to guarantee the SSP property for a larger timestep, in practice using the integrating factor approach by including downwinding as needed with optimal explicit SSP Runge-Kutta methods does not necessarily provide significant benefit over using explicit SSP Runge-Kutta methods with non-decreasing abscissas.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

Improved Collision-Detection Method for Robotic Manipulator

An improved method has been devised for the computational prediction of a collision between (1) a robotic manipulator and (2) another part of the robot or an external object in the vicinity of the robot. The method is intended to be used to test commanded manipulator trajectories in advance so that execution of the commands can be stopped before damage is done. The method involves utilization of both (1) mathematical models of the robot and its environment constructed manually prior to operation and (2) similar models constructed automatically from sensory data acquired during operation. The representation of objects in this method is simpler and more efficient (with respect to both computation time and computer memory), relative to the representations used in most prior methods. The present method was developed especially for use on a robotic land vehicle (rover) equipped with a manipulator arm and a vision system that includes stereoscopic electronic cameras. In this method, objects are represented and collisions detected by use of a previously developed technique known in the art as the method of oriented bounding boxes (OBBs). As the name of this technique indicates, an object is represented approximately, for computational purposes, by a box that encloses its outer boundary. Because many parts of a robotic manipulator are cylindrical, the OBB method has been extended in this method to enable the approximate representation of cylindrical parts by use of octagonal or other multiple-OBB assemblies denoted oriented bounding prisms (OBPs), as in the example of Figure 1. Unlike prior methods, the OBB/OBP method does not require any divisions or transcendental functions; this feature leads to greater robustness and numerical accuracy. The OBB/OBP method was selected for incorporation into the present method because it offers the best compromise between accuracy on the one hand and computational efficiency (and thus computational speed) on the other hand.

Leger, Chris↗

DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows

The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: the second-order Godunov method with PPM interpolation and the high-order finite-volume WENO method. In this work, the results show that while on a smooth problem the high-order method performs better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Improved accuracy for finite element structural analysis via a new integrated force method

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

Patnaik, Surya N.↗

NASA NTRS1992

Improved accuracy for finite element structural analysis via an integrated force method

Patnaik, S. N.↗

NASA NTRS1995

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗