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Further evaluation of traditional icing scaling methods

This report provides additional evaluations of two methods to scale icing test conditions; it also describes a hybrid technique for use when scaled conditions are outside the operating envelope of the test facility. The first evaluation is of the Olsen method which can be used to scale the liquid-water content in icing tests, and the second is the AEDC (Ruff) method which is used when the test model is less than full size. Equations for both scaling methods are presented in the paper, and the methods were evaluated by performing icing tests in the NASA Lewis Icing Research Tunnel (IRT). The Olsen method was tested using 53 cm diameter NACA 0012 airfoils. Tests covered liquid-water-contents which varied by as much as a factor of 1.8. The Olsen method was generally effective in giving scale ice shapes which matched the reference shapes for these tests. The AEDC method was tested with NACA 0012 airfoils with chords from 18 cm to 53 cm. The 53 cm chord airfoils were used in reference tests, and 1/2 and 1/3 scale tests were made at conditions determined by applying the AEDC scaling method. The scale and reference airspeeds were matched in these tests. The AEDC method was found to provide fairly effective scaling for 1/2 size tests, but for 1/3 size models, scaling was generally less effective. In addition to these two scaling methods, a hybrid approach was also tested in which the Olsen method was used to adjust the LWC after size was scaled using the constant Weber number method. This approach was found to be an effective way to test when scaled conditions would otherwise be outside the capability of the test facility.

Anderson, David N.↗

Modified Fully Utilized Design (MFUD) Method for Stress and Displacement Constraints

The traditional fully stressed method performs satisfactorily for stress-limited structural design. When this method is extended to include displacement limitations in addition to stress constraints, it is known as the fully utilized design (FUD). Typically, the FUD produces an overdesign, which is the primary limitation of this otherwise elegant method. We have modified FUD in an attempt to alleviate the limitation. This new method, called the modified fully utilized design (MFUD) method, has been tested successfully on a number of designs that were subjected to multiple loads and had both stress and displacement constraints. The solutions obtained with MFUD compare favorably with the optimum results that can be generated by using nonlinear mathematical programming techniques. The MFUD method appears to have alleviated the overdesign condition and offers the simplicity of a direct, fully stressed type of design method that is distinctly different from optimization and optimality criteria formulations. The MFUD method is being developed for practicing engineers who favor traditional design methods rather than methods based on advanced calculus and nonlinear mathematical programming techniques. The Integrated Force Method (IFM) was found to be the appropriate analysis tool in the development of the MFUD method. In this paper, the MFUD method and its optimality are presented along with a number of illustrative examples.

Patnaik, Surya↗

Bounding Methods for Heterogeneous Lidar-derived Navigational Geofences

Safe Unmanned Aerial Vehicle (UAV) operations near the ground require navigation methods that avoid fixed obstacles such as buildings, power lines and trees. Aerial lidar surveys of ground structures are available with the precision and accuracy to geolocate obstacles, but the high volume of raw survey data can exceed the compute power of onboard processors and the rendering ability of ground-based flight planning maps. Representing ground structures with bounding polyhedra instead of point clouds greatly reduces the data size and can enable effective obstacle avoidance, as long as the bounding geometry envelopes the structures with high spatial fidelity. This report describes in detail four methods to compute bounding geometries of ground obstacles from lidar point clouds. The four methods are: 1) 2.5D Maximum Elevation Box, 2) 2.5D Ground Map Extrusion, 3) 3D Bounding Cylinder, and 4) 3D Bounding Box. The methods are applied to five point cloud datasets from lidar surveys of UAV flight research sites in Georgia and Virginia with an average point spacing that ranges from 0.1m to 0.6m. The methods are assessed using survey areas with geometrically heterogeneous ground structures: buildings, vegetation, power lines, and sub-meter structures such as road signs and guy wires. The 2.5D Maximum Elevation Box method is useful for simple structures. The 2.5D Ground Map Extrusion method efficiently encloses vegetation, but requires handdrawn ground footprints. The 3D Bounding Cylinder method excels at enclosing linear structures such as power lines and fences. The 3D Bounding Box method excels at enclosing planar structures such as buildings. The methods are compared on the basis of data compression and boundary fidelity on selected areas. The 2.5D methods yield the highest data compression but the polyhedra produced by them enclose significant amounts of empty space. Boundary fidelity is superior for the 3D methods, though this fidelity comes at the cost of a roughly thirtyfold lower data compression ratio than the 2.5D Maximum Elevation Box method. A mix of these output geometries is proposed for autonomous UAV navigation with limited on-board computing. Both the accuracy and spatial detail of emerging satellite-based survey technology lower than that of aerial lidar scanning survey technology. Sub-meter structures and thin linear structures are not reliably mapped at present by satellite-based surveys.

Moore, Andrew J.↗

Spectral deferred correction methods for high-order accuracy in poroelastic problems

In this work, we investigate high-order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two-pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two-pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high-order methods are applied to underlying solution strategies, i.e., monolithic, fixed-stress sequential, and undrained sequential methods. We observe that semi-discretized systems from spatial discretization have forms similar to those of index-1 differential algebraic equations (DAEs), causing order reduction against the two-pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second-order accuracy in poroelastic problems while increasing the order of accuracy for index-1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher-order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

02 PETROLEUM↗

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗

Development and Validation of Segmentation Method for Lung Cancer Volumetry on Chest CT

The set of criteria called Response Evaluation Criteria In Solid Tumors (RECIST) is used to evaluate the remedial effects of lung cancer, whereby the size of a lesion can be measured in one dimension (diameter). Volumetric evaluation is desirable for estimating the size of a lesion accurately, but there are several constraints and limitations to calculating the volume in clinical trials. In this study, we developed a method to detect lesions automatically, with minimal intervention by the user, and calculate their volume. Our proposed method, called a spherical region-growing method (SPRG), uses segmentation that starts from a seed point set by the user. SPRG is a modification of an existing region-growing method that is based on a sphere instead of pixels. The SPRG method detects lesions while preventing leakage to neighboring tissues, because the sphere is grown, i.e., neighboring voxels are added, only when all the voxels meet the required conditions. In this study, two radiologists segmented lung tumors using a manual method and the proposed method, and the results of both methods were compared. The proposed method showed a high sensitivity of 81.68–84.81% and a high dice similarity coefficient (DSC) of 0.86–0.88 compared with the manual method. In addition, the SPRG intraclass correlation coefficient (ICC) was 0.998 (CI 0.997–0.999, p < 0.01), showing that the SPRG method is highly reliable. If our proposed method is used for segmentation and volumetric measurement of lesions, then objective and accurate results and shorter data analysis time are possible.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

On the efficiency of different numerical methods for the calculation of intrapulse Raman scattering of optical solitons

In this paper we compare the performance of different numerical methods for the calculation of the asymptotic evolution of soliton self-frequency shift in the presence of intrapulse Raman scattering (IRS) in optical fibers. First we have calculated the order of global accuracy for the fundamental soliton and the second-order bound state of the unperturbed nonlinear Schrödinger equation for the following numerical methods: the simple split step (SS) method, the full SS method, the reduced SS method, the reduced SS method with fourth order Runge–Kutta (RK4), the Blow–Wood method, the fourth order Runge–Kutta in the interaction picture (RK4IP) method and the Agrawal SS method with one and two iterations. We have shown that the asymptotic evolution of soliton self-frequency shift in the presence of IRS in optical fiber can be best described by the Agrawal SS method (compared to the Blow–Wood method and the RK4IP method). The obtained numerical results for the soliton position and frequency are in agreement with the predictions for these parameters according to the perturbation theory. We have shown that in the presence of IRS the fundamental soliton quickly develops an oscillating tail on its left. The generated tail hardly influences the soliton propagation at large distances. At large distances the form of the soliton gradually becomes asymmetric. The increase of the frequency resolution leads to a notable increase of the maximum propagation distance of the numerical soliton under the influence of IRS.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Development and validation of an automatic method to detect the latest contracting viable left ventricular segments to assist guide CRT therapy from gated SPECT myocardial perfusion imaging

Objectives: The purpose of this study is to use ECG-gated SPECT MPI to detect the latest contracting viable left ventricular (LV) segments to help guide the LV probe placement used in CRT therapy and to validate segment selection against the visual integration method by experts. Methods: For each patient, the resting ECG-gated SPECT MPI short-axis images were sampled in 3D to generate a polar map of the perfusion distribution used to determine LV myocardial viability, and to measure LV synchronicity using our phase analysis tool. In the visual integration method, two experts visually interpreted the LV viability and mechanical dyssynchrony from the short-axis images and polar maps of viability and phase, to determine the latest contracting viable segments using the 17-segment model. In the automatic method, the apical segments, septal segments, and segments with more than 50% scar were excluded as these are not candidates for CRT LV probe placement. Amongst the remaining viable segments, the segments, whose phase angles were within 10° of the latest phase angle (the most delayed contracting segment), were identified for potential CRT LV probe placement and ranked based on the phase angles of the segments. Both methods were tested in 36 pre-CRT patients who underwent ECG-gated SPECT MPI. The accuracy was determined as the percent agreement between the visual integration and automatic methods. The automatic method was performed by a second independent operator to evaluate the inter-operator processing reproducibility. Results: In all the 36 patients, the LV lead positions of the 1st choices recommended by the automatic and visual integration methods were in the same segments in 35 patients, which achieved an agreement rate of 97.2%. In the inter-operator reproducibility test, the LV lead positions of the 1st choices recommended by the two operators were in the same segments in 25 patients, and were in the adjacent segments in 7 patients, which achieved an overall agreement of 88.8%. Conclusions: An automatic method has been developed to detect the latest contracting viable LV segments to help guide the LV probe placement used in CRT therapy. The retrospective clinical study with 36 patients suggests that this method has high agreement against the visual integration method by experts and good inter-operator reproducibility. Consequently, this method is promising to be a clinical tool to recommend the CRT LV lead positions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Determination of a suitable molar absorption coefficient (ε) for lignin analysis of fibrous plants using the CASA method

In this study, the benchmarking and applicability of the CASA method for the analysis of fibrous plants, such as flax, hemp, and jute, is evaluated. Lignin is a phenolic biopolymer present in plant cell walls and is composed of three primary monomeric units, designated G, S, and H. Various factors, such as the genetic variability, influence the relative proportions of these units in plant samples. Recently, the cysteine-assisted sulfuric acid (CASA) method has been introduced as a rapid method for the quantification of lignin in wood samples. The aim of this study is to establish a suitable molar absorption coefficient (ε, L·g –1 ·cm –1 ) to adapt the CASA method for use with annual plant fibers. This investigation was motivated by the technical advantages of the CASA method, including higher throughput, lower reaction temperatures, and ecological benefits due to the absence of carcinogenic, mutagenic, or reprotoxic (CMR) substances and the need for minimal sample quantities. In this method, lignin solubilization is facilitated by cysteine, which is an amino acid that enhances the reaction kinetics, using a one-hour incubation period. However, as with any spectrophotometric technique, the CASA method depends on a molar absorption coefficient (ε) that varies according to the ratio of the aromatic units within the polymer. To evaluate the suitability of CASA for quantifying lignin in economically significant plant fibers, we investigate the impact of the unit ratios on the accuracy of ε. The results are compared with those of two widely recognized lignin analytical methods: the Klason method, which is a gravimetric reference method, and the acetyl bromide soluble lignin method, which is the most commonly used spectrophotometric approach. The final ε obtained in this study reveals a relative difference in lignin content ranging from –8 % to +9 % based on a comparison between the CASA and Klason methods across different industrial hemp varieties. As a result, using known G:S ratios in annual fibrous plants, ε can be estimated from our results.

59 BASIC BIOLOGICAL SCIENCES↗

Novel methods for the time-dependent Maxwell's equations and their applications

This dissertation investigates three different mathematical models based on the time-domain Maxwell's equations using three different numerical methods: a Yee scheme using a non-uniform grid, a nodal discontinuous Galerkin (nDG) method, and a newly developed discontinuous Galerkin method named the weak Galerkin (WG) method. The non-uniform Yee scheme is first applied to an electromagnetic metamaterial model. Stability and superconvergence error results are proved for the method, which are then confirmed through numerical results. Additionally, a numerical simulation of backwards wave propagation through a negative-index metamaterial is given using the presented method. Next, the nDG method is used to simulate signal propagation through a corrugated coaxial cable through the use of axisymmetric Maxwell's equations. Stability and error analysis are performed for the semi-discrete method, and are verified through numerical results. The nDG method is then used to simulate signal propagation through coaxial cables with a number of different corrugations. Finally, the WG method is developed for the standard time-domain Maxwell's equations. Similar to the other methods, stability and error analysis are performed on the method and are verified through a number of numerical experiments.

97 MATHEMATICS AND COMPUTING↗

Involute Working Group – FSI Analysis of Fuel Plates Using Finite Volume and Finite Element Methods

The three involute plate research reactors RHF, HFIR, and FRM II have expressed an interest in using computational software to carry their steady-state safety analysis. Since these tools represent a significant departure from the methods used currently (one-dimensional), the acceptability of the new approach by regulators requires thorough verification and validation of these tools. Therefore, Argonne National Laboratory and the three involute-plate reactors formed an informal group called the Involute Working Group aiming at qualifying computational tools to perform steady-state safety analysis. The present report focuses on a comparison of finite volume and finite element methods to model solids in fluid-structure interaction problems with the goal to estimate the coolant flow-induced fuel plate deflections obtained with the two methods. The finite volume method will be obsoleted in STARCCM+ by the end of 2021, nevertheless, this evaluation is important because the method was used by ANL researchers to model the response of the fuel plates, despite its drawbacks, which are discussed in the report. It was essential to check how those estimates compare to the results obtained with the finite element method that is considered superior for structural analysis. Various geometries, i.e., flat, cylindrical and circle-involute fuel plates, as well as coolant flow speed, were considered. The comparison shows that, independently of the plate geometry, the finite volume method significantly underestimates the deflection as compared to finite element method for coarser meshes. When the discretization is developed as a result of a mesh sensitivity study using finite element method, the result obtained using finite volume method can be a few times smaller than the corresponding finite element method solution. A code-to-code comparison , between STAR-CCM+ and LS-DYNA was included in the analysis. Within the LS-DYNA models, two types of finite element formulations were used: solid and shell finite elements. Mesh sensitivity study showed that both approaches converge to a similar value that was obtained with STAR-CCM+ finite element solver. The evaluation of the computational solvers was extended by adding two benchmark cases from the STAR-CCM+ Verification Suite and presented in the Appendix A. The selected cases are: (1) bending of a cantilever beam under external load, and (2) cylindrical shell deformation analysis, known in the literature as ‘Scordelis-Lo roof’. The problems were solved with finite volume, and finite element methods, and the results confirmed the previously discussed findings. The analysis shows that the finite element solver is superior to the finite volume solver in terms of representation of model geometry and estimating the structural behavior of fuel plates. Depending on the ratio of the load to the flexibility of the plate, the finite volume solver can greatly under- or overestimate the structural response if a very carefully selected mesh is not used.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A study of methods which predict supersonic flow fields from body geometry, distance, and Mach number

A study of seven methods for predicting flow-field pressure signatures from the parameters Mach number, body geometry, and field-path distance has been made. The methods included the method of characteristics, which served as a standard of comparison; a shock-capturing method; three Whitham theory methods; a modified characteristics method; and a bicharacteristics method. Results from each method were also compared with recently obtained wind-tunnel data for a cone-cylinder model at Mach numbers of 2.96 and 4.63 with ratios of radial distance to cone length of 2 and 5. The comparisons at a Mach number of 2.96 showed that signatures from all the methods correlated well with wind-tunnel data and with the signatures predicted by the method of characteristics. At a Mach number of 4.63, however, the agreement between the signatures obtained in the wind tunnel and those predicted by theory varied from good to poor, as did the agreement between the signatures obtained by the method of characteristics and the other six methods. It should be noted that these results and comparisons indicate pressure prediction capabilities only for the near-field flow about bodies of revolution.

Mack, R. J.↗

High-frequency asymptotic methods for analyzing the EM scattering by open-ended waveguide cavities

Four high-frequency methods are described for analyzing the electromagnetic (EM) scattering by electrically large open-ended cavities. They are: (1) a hybrid combination of waveguide modal analysis and high-frequency asymptotics, (2) geometrical optics (GO) ray shooting, (3) Gaussian beam (GB) shooting, and (4) the generalized ray expansion (GRE) method. The hybrid modal method gives very accurate results but is limited to cavities which are made up of sections of uniform waveguides for which the modal fields are known. The GO ray shooting method can be applied to much more arbitrary cavity geometries and can handle absorber treated interior walls, but it generally only predicts the major trends of the RCS pattern and not the details. Also, a very large number of rays need to be tracked for each new incidence angle. Like the GO ray shooting method, the GB shooting method can handle more arbitrary cavities, but it is much more efficient and generally more accurate than the GO method because it includes the fields diffracted by the rim at the open end which enter the cavity. However, due to beam divergence effects the GB method is limited to cavities which are not very long compared to their width. The GRE method overcomes the length-to-width limitation of the GB method by replacing the GB's with GO ray tubes which are launched in the same manner as the GB's to include the interior rim diffracted field. This method gives good accuracy and is generally more efficient than the GO method, but a large number of ray tubes needs to be tracked.

Burkholder, R. J.↗

Comparison of advanced reduced-basis methods for transient structural analysis

Two advanced reduced-basis methods for linear, transient structural analysis, the force-derivative method and the Lanczos method, are compared to two widely-used modal methods, the mode-displacement method and the mode-acceleration method. Comparisons are made for two linear example problems: a proportionally-damped cantilevered beam subject to a discrete tip load which varies linearly with time, and a discretely-damped multispan beam subject to a uniformly distributed load which varies as a quintic function of time. Results from the methods are compared in terms of the number of basis vectors required to obtain a desired level of accuracy and the associated computational times. The results are problem dependent, and it is shown that for the cantilevered beam problem, the mode-acceleration and force-derivative methods are the most efficient in terms of the number of basis vectors and computational time. The force-derivative method is shown to be the most effective method for solving the multispan beam problem with closely-spaced frequencies. In general, the force-derivative method is shown to produce an accurate solution using very few basis vectors and to require less computational time as compared to the other methods studied.

Mcgowan, David M.↗

Spectral Methods for Computational Fluid Dynamics

As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral methods in numerical calculations stems from the attractive approximation properties of orthogonal polynomial expansions.

Zang, T. A.↗

Multigrid Methods for EHL Problems

In many bearings and contacts, forces are transmitted through thin continuous fluid films which separate two contacting elements. Objects in contact are normally subjected to friction and wear which can be reduced effectively by using lubricants. If the lubricant film is sufficiently thin to prevent the opposing solids from coming into contact and carries the entire load, then we have hydrodynamic lubrication, where the lubricant film is determined by the motion and geometry of the solids. However, for loaded contacts of low geometrical conformity, such as gears, rolling contact bearings and cams, this is not the case due to high pressures and this is referred to as Elasto-Hydrodynamic Lubrication (EHL) In EHL, elastic deformation of the contacting elements and the increase in fluid viscosity with pressure are very significant and cannot be ignored. Since the deformation results in changing the geometry of the lubricating film, which in turn determines the pressure distribution, an EHL mathematical model must simultaneously satisfy the complex elasticity (integral) and the Reynolds lubrication (differential) equations. The nonlinear and coupled nature of the two equations makes numerical calculations computationally intensive. This is especially true for highly loaded problems found in practice. One novel feature of these problems is that the solution may exhibit sharp pressure spikes in the outlet region. To this date both finite element and finite difference methods have been used to solve EHL problems with perhaps greater emphasis on the use of the finite difference approach. In both cases, a major computational difficulty is ensuring convergence of the nonlinear equations solver to a steady state solution. Two successful methods for achieving this are direct iteration and multigrid methods. Direct iteration methods (e.g Gauss Seidel) have long been used in conjunction with finite difference discretizations on regular meshes. Perhaps one of the best examples of the application of such methods is the recent Effective Influence Method of Dowson and Wang. Multigrid methods have also been used with great success by Venner and Venner and Lubrecht with a good summary being given by Venner. As both these finite difference discretization based approaches appear to provide an efficient way of solving EHL problems, it is important to understand their relative merits. This paper is a first attempt at providing such an understanding in the context of EHL point contact problem, (contact of two spheres), in which the contact zone is a point and an ellipse or circle for unloaded and loaded dry contacts respectively. Since the film thickness and the contact width are generally small compared to the local radius of curvature of the two surfaces, the reduced geometry of the surfaces in the contact area can be accurately approximated to the contact between a paraboloid and a flat surface. The layout of the remainder of this paper is as follows. In section 2 we introduce the form of the equations to be solved. The Effective Influence Newton Method is described in Section 3 while Section 4 describes the Multigrid method to be used. Sections 5 and 6 describe the test problems to be used in the comparison between the two methods and compare the performance of the two methods. Section 7 concludes the paper with an argument of the two methods and suggests some future research directions.

Nurgat, Elyas↗

Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science

Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.

Ransom, Jonathan B.↗

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗