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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A multi-level solution algorithm for steady-state Markov chains

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Horton, Graham↗
NASA NTRS1989

The upwind control volume scheme for unstructured triangular grids

A new algorithm for the numerical solution of the Euler equations is presented. This algorithm is particularly suited to the use of unstructured triangular meshes, allowing geometric flexibility. Solutions are second-order accurate in the steady state. Implementation of the algorithm requires minimal grid connectivity information, resulting in modest storage requirements, and should enhance the implementation of the scheme on massively parallel computers. A novel form of upwind differencing is developed, and is shown to yield sharp resolution of shocks. Two new artificial viscosity models are introduced that enhance the performance of the new scheme. Numerical results for transonic airfoil flows are presented, which demonstrate the performance of the algorithm.

Giles, Michael↗
NASA NTRS1992

Grid generation and its application to separated flows

A method for the computation of recirculating flows on a nonorthogonal boundary-fitted coordinate system is presented. The algebraic grid generation technique is used to generate grids in a flow field of arbitrary shape. Computations are performed by using the set of governing equations transformed for use on a generalized curvilinear coordinate system. Turbulent flow computations were made by using the k-epsilon model for most of the flow cases. Three pressure correction algorithms - SIMPLE, SIMPLEC, and PISO - were incorporated for use on a nonorthogonal grid. Comparisons were made on the basis of numerical stability and accuracy. The present method was found to be efficient for computations of recirculating flows.

Maruszewski, J. P.↗
NASA NTRS1994

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. These algorithms are now used in the practical engineering design of devices such as cars and airplanes as well as theoretical studies of complex phenomena such as fluid turbulence. In past years, limited computer resources have motivated the development of efficient numerical methods in computational fluid dynamics (CFD) utilizing structured meshes. These meshes are comprised of systematic arrays of quadrilateral or hexahedral cells. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Structured meshes also permit the use of highly efficient solution techniques such as alternating direction implicit (ADI) iteration schemes or multigrid. Following the dramatic improvement in computing speed in recent years, emphasis has shifted towards the design of algorithms capable of treating complex geometries. The automatic generation of structured grids about complex geometries is problematic. Unstructured grids offer one promising alternative technique for treating these general geometries. Unstructured meshes have irregular connectivity and usually contain triangles and/or quadrilaterals in two dimensions and tetrahedra and/or hexahedra in three dimensions. The generation and use of unstructured grids poses new challenges in computational fluid dynamics. This is true for both grid generation as well as for the design of algorithms for flow solution. The purpose of these notes is to present recent developments in the unstructured grid generation and flow solution technology.

Barth, T. J.↗
NASA NTRS1973

On the numerical simulation of three-dimensional transonic flow with application to the C-141 wing

Results computed by a finite-difference, relaxation algorithm are presented for the supercritical flow (M = 0.825) about the C-141 airplane wing, which has sweep, taper, and twist. Comparisons with both wind-tunnel and flight data indicate that computed solutions of the classical transonic small disturbance equation can accurately simulate high Reynolds number flows when the shock sweep angle is small. It is also shown that this equation poorly approximates the complete potential equation when embedded shock waves are swept at angles greater than about 15 deg. Hence, a more consistent small disturbance equation is derived for use in more general cases.

Lomax, H.↗
NASA NTRS1975

Hypermatrix scheme for finite element systems on CDC STAR-100 computer

A study is made of the adaptation of the hypermatrix (block matrix) scheme for solving large systems of finite element equations to the CDC STAR-100 computer. Discussion is focused on the organization of the hypermatrix computation using Cholesky decomposition and the mode of storage of the different submatrices to take advantage of the STAR pipeline (streaming) capability. Consideration is also given to the associated data handling problems and the means of balancing the I/Q and cpu times in the solution process. Numerical examples are presented showing anticipated gain in cpu speed over the CDC 6600 to be obtained by using the proposed algorithms on the STAR computer.

Noor, A. K.↗
NASA NTRS1984

Modern Numerical Methods for Classical Sampled System Analysis-SAMSAN

SAMSAN aids control-system analyst by providing self-consistent set of computer algorithms that support large-order control-system design and evaluation studies, with emphasis placed on sampled system analysis. Program provides set of algorithms readily integrated for solving control-system problems.

Frisch, H. P.↗
NASA NTRS1993

A spectral algorithm for envelope reduction of sparse matrices

A new algorithm for reducing the envelope of a sparse matrix is presented. This algorithm is based on the computation of eigenvectors of the Laplacian matrix associated with the graph of the sparse matrix. A reordering of the sparse matrix is determined based on the numerical values of the entries of an eigenvector of the Laplacian matrix. Numerical results show that the new reordering algorithm can in some cases reduce the envelope by more than a factor of two over the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK's reverse Cuthill-McKee (RCM).

Barnard, Stephen T.↗
NASA NTRS1984

Theoretical analysis of aircraft afterbody flow

The strongly interactive flow field about aircraft afterbodies is investigated using computational techniques by which the thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved. A time-dependent implicit numerical algorithm is used to obtain solutions for a variety of afterbody and nozzle geometries, within the class of bodies of revolution, for both subsonic and supersonic external flow, and for sonic and supersonic underexpanded jets. Only centered nozzles with either a sharp lip or a blunt base are considered. In all cases, computed results are compared with experimental data taken at flight Reynolds numbers for like-flow conditions. Turbulence closure is realized using algebraic eddy-viscosity concepts. A new and unique adaptive-grid technique is used to resolve flow regimes with large gradients and to improve the accuracy and efficiency of the computational scheme. Special singular point boundary conditions are used for similar purposes, and are especially effective for highly under-expanded jets. For all cases considered, except one with a very large base-to-nozzle-exit-diameter ratio, the agreement with experimental measurements is excellent. For geometries with large base regions, enhancements in the turbulence transport model are necessary to support improvements in the flow-field simulation.

Deiwert, G. S.↗
NASA NTRS1987

Numerical simulation of single and multiple jet interaction within a combustor

Single and multiple jet interaction in a combustor is simulated numerically to determine the effects of various k-epsilon models and boundary conditions as part of an attempt to understand the physics of the flow field inside the preburner of the Space Shuttle Main Engine. Due to the complexity of the physical and chemical phenomena involved, the model is simplified to two dimensions and a single-component nonreacting fluid. The computer code used is the modified TEACH code, which is a steady state isothermal fluid code using the SIMPLE algorithm. The physical validity and numerical accuracy of the model are established through comparisons with experimentally determined isothermal flow fields in a combustor.

Bai, S. Don↗
NASA NTRS1975

STICAP: A linear circuit analysis program with stiff systems capability. Volume 1: Theory manual

STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given.

Cooke, C. H.↗
NASA NTRS1983

Real gas flow fields about three dimensional configurations

Real gas, inviscid supersonic flow fields over a three-dimensional configuration are determined using a factored implicit algorithm. Air in chemical equilibrium is considered and its local thermodynamic properties are computed by an equilibrium composition method. Numerical solutions are presented for both real and ideal gases at three different Mach numbers and at two different altitudes. Selected results are illustrated by contour plots and are also tabulated for future reference. Results obtained compare well with existing tabulated numerical solutions and hence validate the solution technique.

Balakrishnan, A.↗
NASA NTRS1983

System identification of large flexible structures by using simple continuum models

Simple continuum models for the representation of large truss beams and truss platforms are constructed and employed in the solution of system identification problems permitting the significant reduction of the number of structural parameters. Two simple and easily computer-implemented algorithms are presented for the estimation of a simple model's equivalent structural parameters, and analytical and numerical solutions are given for the truss beam and truss platform cases in order to illustrate the basic concepts. It is found that model simplicity, in conjunction with the principle of least square erors, yields a feasible integration of structural and identification problems.

Juang, J. N.↗
NASA NTRS1984

Flowfield computation of an aerobrake orbital transfer vehicle

Viscous real gas and ideal gas supersonic flowfields over the forebody of a aeroassisted orbital transfer vehicle are determined using a unsteady factored implicit algorithm. Air in chemical equilibrium is considered and its local thermodynamic properties are computed by an equilibrium composition method. Numerical solutions are obtained for both real and ideal gases at a Mach number of 30 and at angles of attack up to 20 degrees. Shock stand-off distances and surface pressure distributions are presented for the gas models with and without viscous effects. For the freestream conditions considered, viscous effects dominate the flow.

Balakrishnan, A.↗
NASA NTRS1992

Accurate ab initio quartic force fields for borane and BeH2

The quartic force fields of BH3 and BeH2 have been computed ab initio using an augmented coupled cluster (CCSD(T)) method and basis sets of spdf and spdfg quality. For BH3, the computed spectroscopic constants are in very good agreement with recent experimental data, and definitively confirm misassignments in some older work, in agreement with recent ab initio studies. Using the computed spectroscopic constants, the rovibrational partition function for both molecules has been constructed using a modified direct numerical summation algorithm, and JANAF-style thermochemical tables are presented.

Martin, J. M. L.↗
NASA NTRS2003

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

Pandya, Shishir A.↗
NASA NTRS2001

Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computations

The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham and Djomehri (1999) aimed at minimizing nu- merical dissipations for high speed compressible viscous flows containing shocks, shears and turbulence. To detect non smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artificial compression method (ACM) of Harten (1978) but utilize it in an entirely different context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem dependence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch to the extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet (Mallat & Zhong 1992) used by Gerritsen and Olsson (1996) in an adaptive mesh refinement method, to determine regions where re nement should be done. The other is the modification of the multiresolution method of Harten (1995) by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen physical quantity (or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these sensors are scheme independent and can be stand alone options for numerical algorithm other than the Yee et al. scheme.

Sjoegreen, B.↗