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NASA NTRS1996

Implicit Extrapolation Methods for Variable Coefficient Problems

Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid tau-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to raise the approximation order, even when the meshes are nonuniform or locally refined. Here previous results are generalized to the variable coefficient case and thus become applicable for nonlinear problems. The implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system. This is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm. The algorithm requires only a small change of a basic low order multigrid method.

Jung, M.↗

NASA NTRS1977

Use of finite element techniques in the determination of the acoustic properties of turbofan inlets

This paper describes the application of the finite-element method in combination with Galerkin's method in the determination of the acoustic properties of turbofan inlets containing high-subsonic-Mach-number flows. An approximate solution to the steady inviscid flow field is obtained using an integral method for calculating the potential flow field in the inlet with a correction to account for compressibility effects. The accuracy of the finite-element technique in predicting the acoustic properties of annular ducts has been checked by comparison with available analytical solutions for the problems of planeand spinning-wave propagation through a hard-walled annular duct with a constant mean flow. Results are presented comparing low-frequency plane-wave propagation through a hard-walled turbofan inlet containing a one-dimensional flow with the same inlet containing a fully two-dimensional axisymmetric mean flow. It is shown that when one-dimensional mean flow is assumed to exist in the duct, the plane wave propagates with relatively little distortion. However, propagation of a plane wave through the fully two-dimensional flow field in the inlet produces severe distortion due to the excitation of higher-order modes.

Sigman, R. K.↗

NASA NTRS1993

An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems

It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.

Cwik, T.↗

NASA NTRS1990

New developments in adaptive methods for computational fluid dynamics

New developments in a posteriori error estimates, smart algorithms, and h- and h-p adaptive finite element methods are discussed in the context of two- and three-dimensional compressible and incompressible flow simulations. Applications to rotor-stator interaction, rotorcraft aerodynamics, shock and viscous boundary layer interaction and fluid-structure interaction problems are discussed.

Oden, J. T.↗

NASA NTRS1978

Application of finite element techniques in predicting the acoustic properties of turbofan inlets

An analytical technique was developed for predicting the acoustic performance of turbofan inlets carrying a subsonic axisymmetric steady flow. The finite element method combined with the method of weighted residuals is used in predicting the acoustic properties of variable area, annular ducts with or without acoustic treatments along their walls. An approximate solution for the steady inviscid flow field is obtained using an integral method for calculating the incompressible potential flow field in the inlet with a correction to account for compressibility effects. The accuracy of the finite element technique was assessed by comparison with available analytical solutions for the problems of plane and spinning wave propagation through a hard walled annular cylinder with a constant mean flow.

Majjigi, R. K.↗

NASA NTRS1993

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Cowsar, Lawrence C.↗

NASA NTRS1972

Two-dimensional finite-element temperature variance analysis

The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.

Heuser, J. S.↗

NASA NTRS1992

Applications of FEM and BEM in two-dimensional fracture mechanics problems

A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.

Min, J. B.↗

NASA NTRS1981

Elasto visco-plastic flow with special attention to boundary conditions

A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

Shimazaki, Y.↗

NASA NTRS1989

Reanalysis, compatibility and correlation in analysis of modified antenna structures

A simple computational procedure is synthesized to process changes in the microwave-antenna pathlength-error measure when there are changes in the antenna structure model. The procedure employs structural modification reanalysis methods combined with new extensions of correlation analysis to provide the revised rms pathlength error. Mainframe finite-element-method processing of the structure model is required only for the initial unmodified structure, and elementary postprocessor computations develop and deal with the effects of the changes. Several illustrative computational examples are included. The procedure adapts readily to processing spectra of changes for parameter studies or sensitivity analyses.

Levy, R.↗

NASA NTRS1990

A Finite Element Procedure for Calculating Fluid-Structure Interaction Using MSC/NASTRAN

This report is intended to serve two purposes. The first is to present a survey of the theoretical background of the dynamic interaction between a non-viscid, compressible fluid and an elastic structure is presented. Section one presents a short survey of the application of the finite element method (FEM) to the area of fluid-structure-interaction (FSI). Section two describes the mathematical foundation of the structure and fluid with special emphasis on the fluid. The main steps in establishing the finite element (FE) equations for the fluid structure coupling are discussed in section three. The second purpose is to demonstrate the application of MSC/NASTRAN to the solution of FSI problems. Some specific topics, such as fluid structure analogy, acoustic absorption, and acoustic contribution analysis are described in section four. Section five deals with the organization of the acoustic procedure flowchart. Section six includes the most important information that a user needs for applying the acoustic procedure to practical FSI problems. Beginning with some rules concerning the FE modeling of the coupled system, the NASTRAN USER DECKs for the different steps are described. The goal of section seven is to demonstrate the use of the acoustic procedure with some examples. This demonstration includes an analytic verification of selected FE results. The analytical description considers only some aspects of FSI and is not intended to be mathematically complete. Finally, section 8 presents an application of the acoustic procedure to vehicle interior acoustic analysis with selected results.

Chargin, Mladen↗

NASA NTRS1994

Non-Reflecting Regions for Finite Difference Methods in Modeling of Elastic Wave Propagation in Plates

Solution of the wave equation using techniques such as finite difference or finite element methods can model elastic wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.

Kishoni, Doron↗

NASA NTRS1996

Analytical Fuselage and Wing Weight Estimation of Transport Aircraft

A method of estimating the load-bearing fuselage weight and wing weight of transport aircraft based on fundamental structural principles has been developed. This method of weight estimation represents a compromise between the rapid assessment of component weight using empirical methods based on actual weights of existing aircraft, and detailed, but time-consuming, analysis using the finite element method. The method was applied to eight existing subsonic transports for validation and correlation. Integration of the resulting computer program, PDCYL, has been made into the weights-calculating module of the AirCraft SYNThesis (ACSYNT) computer program. ACSYNT has traditionally used only empirical weight estimation methods; PDCYL adds to ACSYNT a rapid, accurate means of assessing the fuselage and wing weights of unconventional aircraft. PDCYL also allows flexibility in the choice of structural concept, as well as a direct means of determining the impact of advanced materials on structural weight. Using statistical analysis techniques, relations between the load-bearing fuselage and wing weights calculated by PDCYL and corresponding actual weights were determined.

Chambers, Mark C.↗

NASA NTRS1996

Active Control of Fan Noise: Feasibility Study: Numerical Computation of Acoustic Mode Reflection Coefficients for an Unflanged Cylindrical Duct - Volume 5

A computational method to predict modal reflection coefficients in cylindrical ducts has been developed based on the work of Homicz, Lordi, and Rehm, which uses the Wiener-Hopf method to account for the boundary conditions at the termination of a thin cylindrical pipe. The purpose of this study is to develop a computational routine to predict the reflection coefficients of higher order acoustic modes impinging on the unflanged termination of a cylindrical duct. This effort was conducted wider Task Order 5 of the NASA Lewis LET Program, Active Noise Control of aircraft Engines: Feasibility Study, and will be used as part of the development of an integrated source noise, acoustic propagation, ANC actuator coupling, and control system algorithm simulation. The reflection coefficient prediction will be incorporated into an existing cylindrical duct modal analysis to account for the reflection of modes from the duct termination. This will provide a more accurate, rapid computation design tool for evaluating the effect of reflected waves on active noise control systems mounted in the duct, as well as providing a tool for the design of acoustic treatment in inlet ducts. As an active noise control system design tool, the method can be used preliminary to more accurate but more numerically intensive acoustic propagation models such as finite element methods. The resulting computer program has been shown to give reasonable results, some examples of which are presented. Reliable data to use for comparison is scarce, so complete checkout is difficult, and further checkout is needed over a wider range of system parameters. In future efforts the method will be adapted as a subroutine to the GEAE segmented cylindrical duct modal analysis program.

Kraft, R. E.↗

NASA NTRS1996

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

In this report the author describes: (1) development of advanced methods of structural weight estimation, and (2) development of advanced methods of flight path optimization. A method of estimating the load-bearing fuselage weight and wing weight of transport aircraft based on fundamental structural principles has been developed. This method of weight estimation represents a compromise between the rapid assessment of component weight using empirical methods based on actual weights of existing aircraft and detailed, but time-consuming, analysis using the finite element method. The method was applied to eight existing subsonic transports for validation and correlation. Integration of the resulting computer program, PDCYL, has been made into the weights-calculating module of the AirCraft SYNThesis (ACSYNT) computer program. ACSYNT bas traditionally used only empirical weight estimation methods; PDCYL adds to ACSYNT a rapid, accurate means of assessing the fuselage and wing weights of unconventional aircraft. PDCYL also allows flexibility in the choice of structural concept, as well as a direct means of determining the impact of advanced materials on structural weight.

Ardema, Mark D.↗

NASA NTRS1996

Multigrid and Krylov Subspace Methods for Transport Equations: Absorption Case

In this paper we look at Krylov subspace methods for solving the transport equations in a slab geometry. The spatial discretization scheme used is a finite element method called Modified Linear Discontinuous scheme (MLD). We investigate the convergence rates for a number of Krylov subspace methods for this problem and compare with the results of a spatial multigrid scheme.

Oliveira, S.↗

DOE OSTI2025

A stable potential-based time-domain method for wideband elec- tromagnetic analysis

In previous research, the frequency-domain A-ϕ formulation has been validated using the finite element method for electromagnetic simulations of low-frequency and multi- scale problems, demonstrating excellent numerical accuracy, good matrix condition, and high computational efficiency. Time- domain simulations provide significant advantages for modeling wideband problems and are crucial for multiphysics applications. In this paper, the frequency-domain A-ϕ formulation is extended to the time domain. The central difference scheme is employed for temporal discretization to ensure both accuracy and stability. A numerical example is presented to demonstrate the capability of the proposed time-domain method in wideband electromagnetic analysis.

Mekonnen, Minyichil↗

NASA NTRS1985

Theoretical and software considerations for general dynamic analysis using multilevel substructured models

The dynamic analysis of complex structural systems using the finite element method and multilevel substructured models is presented. The fixed-interface method is selected for substructure reduction because of its efficiency, accuracy, and adaptability to restart and reanalysis. This method is extended to reduction of substructures which are themselves composed of reduced substructures. The implementation and performance of the method in a general purpose software system is emphasized. Solution algorithms consistent with the chosen data structures are presented. It is demonstrated that successful finite element software requires the use of software executives to supplement the algorithmic language. The complexity of the implementation of restart and reanalysis porcedures illustrates the need for executive systems to support the noncomputational aspects of the software. It is shown that significant computational efficiencies can be achieved through proper use of substructuring and reduction technbiques without sacrificing solution accuracy. The restart and reanalysis capabilities and the flexible procedures for multilevel substructured modeling gives economical yet accurate analyses of complex structural systems.

Schmidt, R. J.↗