Assessing the Iterative Finite Difference Mass Balance and 4D‐Var Methods to Derive Ammonia Emissions Over North America Using Synthetic Observations
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Chi Li↗
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Results for “Iteration method”
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Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations
A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.
Johnson, Forrester T.↗
Flux vector splitting and approximate Newton methods
In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocity-sound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasi-one-dimensional flow in a nozzle. Results are given for steady flows with shocks.
Jespersen, D. C.↗
Optimization of OT-MACH Filter Generation for Target Recognition
An automatic Optimum Trade-off Maximum Average Correlation Height (OT-MACH) filter generator for use in a gray-scale optical correlator (GOC) has been developed for improved target detection at JPL. While the OT-MACH filter has been shown to be an optimal filter for target detection, actually solving for the optimum is too computationally intensive for multiple targets. Instead, an adaptive step gradient descent method was tested to iteratively optimize the three OT-MACH parameters, alpha, beta, and gamma. The feedback for the gradient descent method was a composite of the performance measures, correlation peak height and peak to side lobe ratio. The automated method generated and tested multiple filters in order to approach the optimal filter quicker and more reliably than the current manual method. Initial usage and testing has shown preliminary success at finding an approximation of the optimal filter, in terms of alpha, beta, gamma values. This corresponded to a substantial improvement in detection performance where the true positive rate increased for the same average false positives per image.
false alarm reduction↗
Relaxation methods in fluid mechanics
The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.
Lomax, H.↗
A possibilistic approach to clustering
Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering methods in that total commitment of a vector to a given class is not required at each image pattern recognition iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from the 'Fuzzy C-Means' (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Recently, we cast the clustering problem into the framework of possibility theory using an approach in which the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We show the ability of this approach to detect linear and quartic curves in the presence of considerable noise.
Krishnapuram, Raghu↗
The CLASSY clustering algorithm: Description, evaluation, and comparison with the iterative self-organizing clustering system (ISOCLS)
A clustering method, CLASSY, was developed, which alternates maximum likelihood iteration with a procedure for splitting, combining, and eliminating the resulting statistics. The method maximizes the fit of a mixture of normal distributions to the observed first through fourth central moments of the data and produces an estimate of the proportions, means, and covariances in this mixture. The mathematical model which is the basic for CLASSY and the actual operation of the algorithm is described. Data comparing the performances of CLASSY and ISOCLS on simulated and actual LACIE data are presented.
Lennington, R. K.↗
Rapid finite-difference computation of subsonic and transonic aerodynamic flows
Rapid iterative (or semidirect) computation methods are developed for the finite-difference solution of the nonlinear equations of subsonic and transonic aerodynamics. At each iteration, a fast, direct elliptic algorithm solves the entire computation field. In an application to subsonic flow over a lifting airfoil, the full nonlinear stream-function equation is solved. Finally, a direct Cauchy-Riemann solver is used for the nonlinear transonic small-disturbance equations for a biconvex airfoil. At M = 0.7, t/c = 0.1 (subcritical), three iterations on a 39 x 32 mesh (totaling 2.45 sec on an IBM 360/67 computer) obtain convergence within 0.1%. A slightly supercritical case requires seven iterations (6.75 sec) for convergence within 1%.
Martin, E. D.↗
Computational Investigation of a Boundary-Layer Ingestion Propulsion System for the Common Research Model
This thesis will examine potential propulsive and aerodynamic benefits of integrating a boundary-layer ingestion (BLI) propulsion system with a typical commercial aircraft using the Common Research Model geometry and the NASA Tetrahedral Unstructured Software System (TetrUSS). The Numerical Propulsion System Simulation (NPSS) environment will be used to generate engine conditions for CFD analysis. Improvements to the BLI geometry will be made using the Constrained Direct Iterative Surface Curvature (CDISC) design method. Previous studies have shown reductions of up to 25% in terms of propulsive power required for cruise for other axisymmetric geometries using the BLI concept. An analysis of engine power requirements, drag, and lift coefficients using the baseline and BLI geometries coupled with the NPSS model are shown. Potential benefits of the BLI system relating to cruise propulsive power are quantified using a power balance method and a comparison to the baseline case is made. Iterations of the BLI geometric design are shown and any improvements between subsequent BLI designs presented. Simulations are conducted for a cruise flight condition of Mach 0.85 at an altitude of 38,500 feet and an angle of attack of 2deg for all geometries. A comparison between available wind tunnel data, previous computational results, and the original CRM model is presented for model verification purposes along with full results for BLI power savings. Results indicate a 14.3% reduction in engine power requirements at cruise for the BLI configuration over the baseline geometry. Minor shaping of the aft portion of the fuselage using CDISC has been shown to increase the benefit from boundary-layer ingestion further, resulting in a 15.6% reduction in power requirements for cruise as well as a drag reduction of eighteen counts over the baseline geometry.
Blumenthal, Brennan↗
Computational Investigation of a Boundary-Layer Ingesting Propulsion System for the Common Research Model
The present paper examines potential propulsive and aerodynamic benefits of integrating a Boundary-Layer Ingestion (BLI) propulsion system into a typical commercial aircraft using the Common Research Model (CRM) geometry and the NASA Tetrahedral Unstructured Software System (TetrUSS). The Numerical Propulsion System Simulation (NPSS) environment is used to generate engine conditions for CFD analysis. Improvements to the BLI geometry are made using the Constrained Direct Iterative Surface Curvature (CDISC) design method. Previous studies have shown reductions of up to 25% in terms of propulsive power required for cruise for other axisymmetric geometries using the BLI concept. An analysis of engine power requirements, drag, and lift coefficients using the baseline and BLI geometries coupled with the NPSS model are shown. Potential benefits of the BLI system relating to cruise propulsive power are quantified using a power balance method, and a comparison to the baseline case is made. Iterations of the BLI geometric design are shown and any improvements between subsequent BLI designs presented. Simulations are conducted for a cruise flight condition of Mach 0.85 at an altitude of 38,500 feet and an angle of attack of 2 deg for all geometries. A comparison between available wind tunnel data, previous computational results, and the original CRM model is presented for model verification purposes along with full results for BLI power savings. Results indicate a 14.4% reduction in engine power requirements at cruise for the BLI configuration over the baseline geometry. Minor shaping of the aft portion of the fuselage using CDISC has been shown to increase the benefit from Boundary-Layer Ingestion further, resulting in a 15.6% reduction in power requirements for cruise as well as a drag reduction of eighteen counts over the baseline geometry.
Blumenthal, Brennan T.↗
A fast operator perturbation method for the solution of the special relativistic equation of radiative transfer in spherical symmetry
A fast method for the solution of the radiative transfer equation in rapidly moving spherical media, based on an approximate Lambda-operator iteration, is described. The method uses the short characteristic method and a tridiagonal approximate Lambda-operator to achieve fast convergence. The convergence properties and the CPU time requirements of the method are discussed for the test problem of a two-level atom with background continuum absorption and Thomson scattering. Details of the actual implementation for fast vector and parallel computers are given. The method is accurate and fast enough to be incorporated in radiation-hydrodynamic calculations.
Hauschildt, P. H.↗
An efficient numerical algorithm for transverse impact problems
Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.
Sankar, B. V.↗
Improved method for solving the viscous shock layer equations
An improved method for solving the viscous shock layer equations for supersonic/hypersonic flows past blunt-nosed bodies is presented. The method is capable of handling slender to thick bodies. The solution is obtained by solving a coupled set of five equations, built of the four basic viscous shock layer equations and an additional equation for the standoff distance. The coupling of the equations prevents the local iterations divergence problems encountered by previous methods of solution far downstream on slender bodies. It also eliminates the need for local iterations, which were required by previous methods of solution, for a first-order scheme in the streamwise direction. A new global iteration procedure is employed to impose the shock boundary conditions. The procedure prevents the global iteration instability encountered by the basic method of solution and improves the convergence rate of the global iteration procedure of later methods devised to overcome this difficulty. The new technique reduces the computation time by 65-95 percent as compared to previous methods of solution. The method can efficiently be implemented in vector/parallel computers.
Gordon, Rachel↗
Stress analysis method for clearance-fit joints with bearing-bypass loads
Within a multi-fastener joint, fastener holes may be subjected to the combined effects of bearing loads and loads that bypass the hole to be reacted elsewhere in the joint. The analysis of a joint subjected to search combined bearing and bypass loads is complicated by the usual clearance between the hole and the fastener. A simple analysis method for such clearance-fit joints subjected to bearing-bypass loading has been developed in the present study. It uses an inverse formulation with a linear elastic finite-element analysis. Conditions along the bolt-hole contact arc are specified by displacement constraint equations. The present method is simple to apply and can be implemented with most general purpose finite-element programs since it does not use complicated iterative-incremental procedures. The method was used to study the effects of bearing-bypass loading on bolt-hole contact angles and local stresses. In this study, a rigid, frictionless bolt was used with a plate having the properties of a quasi-isotropic graphite/epoxy laminate. Results showed that the contact angle as well as the peak stresses around the hole and their locations were strongly influenced by the ratio of bearing and bypass loads. For single contact, tension and compression bearing-bypass loading had opposite effects on the contact angle. For some compressive bearing-bypass loads, the hole tended to close on the fastener leading to dual contact. It was shown that dual contact reduces the stress concentration at the fastener and would, therefore, increase joint strength in compression. The results illustrate the general importance of accounting for bolt-hole clearance and contact to accurately compute local bolt-hole stresses for combined bearings and bypass loading.
Naik, R. A.↗
Regression Analysis and Calibration Recommendations for the Characterization of Balance Temperature Effects
Analysis and use of temperature-dependent wind tunnel strain-gage balance calibration data are discussed in the paper. First, three different methods are presented and compared that may be used to process temperature-dependent strain-gage balance data. The first method uses an extended set of independent variables in order to process the data and predict balance loads. The second method applies an extended load iteration equation during the analysis of balance calibration data. The third method uses temperature-dependent sensitivities for the data analysis. Physical interpretations of the most important temperature-dependent regression model terms are provided that relate temperature compensation imperfections and the temperature-dependent nature of the gage factor to sets of regression model terms. Finally, balance calibration recommendations are listed so that temperature-dependent calibration data can be obtained and successfully processed using the reviewed analysis methods.
wind tunnel test↗
A Numerical Theory for Impedance Education in Three-Dimensional Normal Incidence Tubes
A method for educing the locally-reacting acoustic impedance of a test sample mounted in a 3-D normal incidence impedance tube is presented and validated. The unique feature of the method is that the excitation frequency (or duct geometry) may be such that high-order duct modes may exist. The method educes the impedance, iteratively, by minimizing an objective function consisting of the difference between the measured and numerically computed acoustic pressure at preselected measurement points in the duct. The method is validated on planar and high-order mode sources with data synthesized from exact mode theory. These data are then subjected to random jitter to simulate the effects of measurement uncertainties on the educed impedance spectrum. The primary conclusions of the study are 1) Without random jitter the method is in excellent agreement with that for known impedance samples, and 2) Random jitter that is compatible to that found in a typical experiment has minimal impact on the accuracy of the educed impedance.
Watson, Willie R.↗
Mesh generation/refinement using fractal concepts and iterated function systems
A novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3D tesselation.
Bova, S. W.↗
Possibilistic clustering for shape recognition
Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, we cast the clustering problem into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We constructed an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derived the membership and prototype update equations from necessary conditions for minimization of our criterion function. In this paper, we show the ability of this approach to detect linear and quartic curves in the presence of considerable noise.
Keller, James M.↗