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At least 199 records · Page 11
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NASA NTRS1988

Modal cost analysis for simple continua

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations, it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for simple continua such as beam-like structures. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗
NASA NTRS1988

VLBI studies of the nutations of the earth

The analysis of six years of VLBI data has yielded corrections to the coefficients of the seven largest terms in the IAU 1980 nutation series with periods of one year or less, with accuracies approaching the truncation error of this nutation series (0.1 mas). This paper examines the methods used to extract the nutation information from the VLBI data, the calculation of the uncertanties of the resultant corrections to the nutation-series coefficients, and current research on the earth's nutations.

Herring, T. A.↗
NASA NTRS1989

Application of a self-adaptive grid method to complex flows

A directional-split, modular, user-friendly grid point distribution code is applied to several test problems. The code is self-adaptive in the sense that grid point spacing is determined by user-specified constants denoting maximum and minimum grid spacings and constants relating the relative influence of smoothness and orthogonality. Estimates of truncation error, in terms of flow-field gradients and/or geometric features, are used to determine the point distribution. Points are redistributed along grid lines in a specified direction in an elliptic manner over a user-specified subdomain, while orthogonality and smoothness are controlled in a parabolic (marching) manner in the remaining directions. Multidirectional adaption is achieved by sequential application of the method in each coordinate direction. The flow-field solution is redistributed onto the newly distributed grid points after each unidirectional adaption by a simple one-dimensional interpolation scheme. For time-accurate schemes such interpolation is not necessary and time-dependent metrics are carried in the fluid dynamic equations to account for grid movement.

Deiwert, G. S.↗
NASA NTRS1990

High accuracy solutions of incompressible Navier-Stokes equations

In recent years, high accuracy finite difference approximations were developed for partial differential equations of elliptic type, with particular emphasis on the convection-diffusion equation. These approximations are of compact type, have a local truncation error of fourth order, and allow the use of standard iterative schemes to solve the resulting systems of algebraic equations. These high accuracy approximations are extended to the solution of Navier-Stokes equations. Solutions are obtained for the model problem of driven cavity and are compared with solutions obtained using other approximations and those obtained by other authors. It is discovered that the high order approximations do indeed produce high accuracy solutions and have a potential for use in solving important problems of viscous fluid flows.

Gupta, Murli M.↗
NASA NTRS1989

Application of a self-adaptive grid method to complex flows

A directional-split modular user-friendly grid-point distribution code is applied to several test problems. Grid-point spacing is determined by user-specified constants denoting maximum and minimum grid spacings and relating the relative influence of smoothness and orthogonality. Estimates of truncation error, in terms of flowfield gradients and/or geometric features, are used to determine the point distribution.

Deiwert, G. S.↗
NASA NTRS1990

The 'optimum' upwind advection on a triangular mesh

For advection schemes based on fluctuation splitting, a design criterion of optimizing the time step leads to linear schemes that coincide with those designed for least truncation error. A further stage of optimizing the time step using a nonlinear positivity criterion, leads to considerable further gains in resolution.

Roe, P. L.↗
NASA NTRS1990

Formulation of boundary conditions for the multigrid acceleration of the Euler and Navier Stokes equations

An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.

Jentink, Thomas Neil↗
NASA NTRS1990

Estimation of UH-60 blade aerodynamic loads and rotor impedance using generalized strain pattern/Kalman filter approach

The purpose of the study is to develop and verify a methodology capable of predicting the vibration levels and estimating the aerodynamic loads and rotor impedance of a rotorcraft blade. Simulated flight test data is generated, blade airloads and elastic hub motions are estimated from the simulated data through the use of the Kalman filter/smoother, simulation upgrading and parameter identification are performed, and the ability to identify rotor impedance from a simulation by isolating the rotor model and providing a prescribed motion for the hub as rotor excitation is demonstrated. It is pointed out that the statistical estimation procedure utilized in the proposed methodology minimizes the impact of sensor noise, truncation error, and instrumentation bias on the results.

Bruhis, Ofer↗
NASA NTRS1990

Numerical experiments on the accuracy of ENO and modified ENO schemes

Numerical experiments have been performed using different ENO schemes and different time discretizations, in order to assess accuracy-degeneracy phenomena of the type described by Rogerson and Meiburg (1990). A modified ENO scheme recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives results comparable to the original ENO schemes for discontinuous problems. It is concluded that ENO schemes may lose the full high-order accuracy predicted by local truncation-error analysis for scalar linear conservation laws with smooth initial conditions. A modified ENO scheme can overcome this accuracy-degeneracy problem for the test problems without increasing the computational cost.

Shu, Chi-Wang↗
NASA NTRS1992

An efficient HZETRN (a galactic cosmic ray transport code)

An accurate and efficient engineering code for analyzing the shielding requirements against the high-energy galactic heavy ions is needed. The HZETRN is a deterministic code developed at Langley Research Center that is constantly under improvement both in physics and numerical computation and is targeted for such use. One problem area connected with the space-marching technique used in this code is the propagation of the local truncation error. By improving the numerical algorithms for interpolation, integration, and grid distribution formula, the efficiency of the code is increased by a factor of eight as the number of energy grid points is reduced. The numerical accuracy of better than 2 percent for a shield thickness of 150 g/cm(exp 2) is found when a 45 point energy grid is used. The propagating step size, which is related to the perturbation theory, is also reevaluated.

Shinn, Judy L.↗
NASA NTRS1992

Cartesian based grid generation/adaptive mesh refinement

Grid adaptation has recently received attention in the computational fluid dynamics (CFD) community as a means to capture the salient features of a flowfield by either moving grid points of a structured or by adding cells in an unstructured manner. An approach based on a background cartesian mesh is investigated from which the geometry is 'cut' out of the mesh. Once the mesh is obtained, a solution on this coarse grid is found, that indicates which cells need to be refined. This process of refining/solving continues until the flow is grid refined in terms of a user specified global parameter (such as drag coefficient etc.). The advantages of this approach are twofold: the generation of the base grid is independent of the topology of the bodies or surfaces around/through which the flow is to be computed, and the resulting grid (in uncut regions) is highly isotropic, so that the truncation error is low. The flow solver (which, along with the grid generation is still under development) uses a completely unstructured data base, and is a finite volume, upwinding scheme. Current and future work will address generating Navier-Stokes suitable grids by using locally aligned and normal face/cell refining. The attached plot shows a simple grid about two turbine blades.

Coirier, William J.↗
NASA NTRS1992

The F(N) method for the one-angle radiative transfer equation applied to plant canopies

The paper presents a semianalytical solution method, called the F(N) method, for the one-angle radiative transfer equation in slab geometry. The F(N) method is based on two integral equations specifying the intensities exiting the boundaries of the vegetation canopy; the solution is obtained through an expansion in a set of basis functions with expansion coefficients to be determined. The advantage of this method is that it avoids spatial truncation error entirely because it requires discretization only in the angular variable.

Ganapol, B. D.↗
NASA NTRS1993

Analysis of the Space Shuttle main engine simulation

This is a final report on an analysis of the Space Shuttle Main Engine Program, a digital simulator code written in Fortran. The research was undertaken in ultimate support of future design studies of a shuttle life-extending Intelligent Control System (ICS). These studies are to be conducted by NASA Lewis Space Research Center. The primary purpose of the analysis was to define the means to achieve a faster running simulation, and to determine if additional hardware would be necessary for speeding up simulations for the ICS project. In particular, the analysis was to consider the use of custom integrators based on the Matrix Stability Region Placement (MSRP) method. In addition to speed of execution, other qualities of the software were to be examined. Among these are the accuracy of computations, the useability of the simulation system, and the maintainability of the program and data files. Accuracy involves control of truncation error of the methods, and roundoff error induced by floating point operations. It also involves the requirement that the user be fully aware of the model that the simulator is implementing.

Deabreu-Garcia, J. Alex↗
NASA NTRS1993

The three-dimensional Multi-Block Advanced Grid Generation System (3DMAGGS)

As the size and complexity of three dimensional volume grids increases, there is a growing need for fast and efficient 3D volumetric elliptic grid solvers. Present day solvers are limited by computational speed and do not have all the capabilities such as interior volume grid clustering control, viscous grid clustering at the wall of a configuration, truncation error limiters, and convergence optimization residing in one code. A new volume grid generator, 3DMAGGS (Three-Dimensional Multi-Block Advanced Grid Generation System), which is based on the 3DGRAPE code, has evolved to meet these needs. This is a manual for the usage of 3DMAGGS and contains five sections, including the motivations and usage, a GRIDGEN interface, a grid quality analysis tool, a sample case for verifying correct operation of the code, and a comparison to both 3DGRAPE and GRIDGEN3D. Since it was derived from 3DGRAPE, this technical memorandum should be used in conjunction with the 3DGRAPE manual (NASA TM-102224).

Alter, Stephen J.↗
NASA NTRS1993

Finite element/finite volume approaches with adaptive time stepping strategies for transient thermal problems

An adaptive time stepping strategy for transient thermal analysis of engineering systems is described which computes the time step based on the local truncation error with a good global error control and obtains optimal time steps to be used during the analysis. Combined mesh partitionings involving FEM/FVM meshes based on physical situations to obtain numerically improved physical representations are also proposed. Numerical test cases are described and comparative pros and cons are identified for practical situations.

Mohan, Ram V.↗
NASA NTRS1993

Euler solutions for blunt bodies using triangular meshes - Artificial viscosity forms and numerical boundary conditions

A finite volume method is used to calculate compressible inviscid flows over blunt bodies using, in general, unstructured grids. Artificial viscosity forms are derived based on a simplified least squares procedure. The extra second order terms are consistent with the governing equations, hence a systematic treatment of the numerical boundary conditions can be easily implemented. A special treatment of blunt bodies may be required. The discrete equations are linearized and the resulting system is solved by a relaxation method. Preliminary results indicate that the effect of the numerical dissipation is minimal. For subsonic flows over smooth bodies, the solution is practically vorticity-free and the total pressure loss is of the same order as the truncation error. Finally, some extensions of the present method are briefly discussed.

Winterstein, R.↗
NASA NTRS1993

Analysis of implicit second-order upwind-biased stencils

Truncation error and stability properties of several implicit upwind schemes for the two-dimensional Euler equations are examined. The schemes use linear data reconstruction methods to achieve second-order flux integrations where the implicit Jacobian operators are first order. The stability properties of the schemes are examined by a Von Neumann analysis of the linearized, constant-coefficient Euler equations. The choice of the data reconstruction method used to evaluate the flux integral has a dramatic effect on the convergence properties of the implicit solution method. In particular, the typical one-dimensional data reconstruction methods used with structured grids exhibit poor convergence properties compared to the unstructured grid method considered. Of the schemes examined, the one with the superior convergence properties is well-suited for both unstructured and structured grids, which has important implications for the design of implicit methods.

Roberts, Thomas W.↗
NASA NTRS1989

Numerical simulation of controlled large space structures

Large Space Structures do not have much damping, which necessitates the installation of a controller onto the structure. If the controller is improperly designed, the structure may become unstable and be destroyed. Since Large Space Structures are extremely expensive pieces of hardware, new controllers must not be tested first on the structure. They must first be tested in computer simulations. Until now, the usual procedure for simulating controlled Large Space Structures is to compute a reduced order modal representation of the structure and then apply the controller. However, this procedure entails modal truncation error. A new software package which is free from this error is currently under development within the Center for Space Construction. The more accurate finite element representation of the structure is used in the simulation, instead of the less accurate reduced order modal representation. This software also features an efficient matrix storage scheme, which effectively deals with the asymmetric system matrices which occur when control is added to the structure. Also, an integration algorithm was chosen so that the simulation is a reliable indicator of system stability or instability. The software package is fairly general in nature. Linearity of the finite element model and of the controller is the only assumption made. Actuator dynamics, sensor dynamics, noise, and disturbances can be handled by the package. In addition, output feedback of displacement, velocity, and/or acceleration signals can be simulated. Kalman state estimation was also implemented. This software was tested on a finite element model of a real Large Space Structure: The Mini-Mast Truss. Mini-Mast is a testbed at NASA-Langley which is currently under development. A 714 degree of freedom finite element model was computed, and a 19 state controller was designed for it. Torque wheel dynamics were added to the model, and the entire closed loop system was simulated with the software package.

Quan, Ralph↗