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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Shock capturing finite difference algorithms for supersonic flow past fighter and missile type configurations

The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.

Osher, S.↗
NASA NTRS1995

Nonstandard finite difference schemes

The major research activities of this proposal center on the construction and analysis of nonstandard finite-difference schemes for ordinary and partial differential equations. In particular, we investigate schemes that either have zero truncation errors (exact schemes) or possess other significant features of importance for numerical integration. Our eventual goal is to bring these methods to bear on problems that arise in the modeling of various physical, engineering, and technological systems. At present, these efforts are extended in the direction of understanding the exact nature of these nonstandard procedures and extending their use to more complicated model equations. Our presentation will give a listing (obtained to date) of the nonstandard rules, their application to a number of linear and nonlinear, ordinary and partial differential equations. In certain cases, numerical results will be presented.

Mickens, Ronald E.↗
NASA NTRS1999

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Kouatchou, Jules↗
NASA NTRS2005

FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates

A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.

Kaul, Upender K.↗
NASA NTRS2016

Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids

Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.

Overset Grids↗
NASA NTRS1993

Acceleration of convergence and spectrum transformation of implicit finite difference operators associated with Navier-Stokes equations

Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.

Saleem, M.↗
NASA NTRS1974

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.↗
NASA NTRS1976

A two-dimensional finite difference solution for the transient thermal behavior of tubular solar collector

A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique was analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

Lansing, F. L.↗
NASA NTRS1960

Applications of a General Finite-Difference Method for Calculating Bending Deformations of Solid Plates

This paper reports the findings of an investigation of a finite - difference method directly applicable to calculating static or simple harmonic flexures of solid plates and potentially useful in other problems of structural analysis. The method, which was proposed in doctoral thesis by John C. Houbolt, is based on linear theory and incorporates the principle of minimum potential energy. Full realization of its advantages requires use of high-speed computing equipment. After a review of Houbolt's method, results of some applications are presented and discussed. The applications consisted of calculations of the natural modes and frequencies of several uniform-thickness cantilever plates and, as a special case of interest, calculations of the modes and frequencies of the uniform free-free beam. Computed frequencies and nodal patterns for the first five or six modes of each plate are compared with existing experiments, and those for one plate are compared with another approximate theory. Beam computations are compared with exact theory. On the basis of the comparisons it is concluded that the method is accurate and general in predicting plate flexures, and additional applications are suggested. An appendix is devoted t o computing procedures which evolved in the progress of the applications and which facilitate use of the method in conjunction with high-speed computing equipment.

Walton, William C., Jr.↗
NASA NTRS1974

A study of three finite-difference schemes and their role in asynoptic meteorological data assimilation

An investigation was conducted concerning the response of various finite-difference schemes to the insertion of unweighted data. A simple barotropic model was employed as a forecast model. The Mintz-Arakawa two-level general circulation model was used as a source of data. The schemes tested include a Shuman scheme employing centered time differences and 9-point spatial smoothing. Two other schemes investigated were a Matsuno-TASU scheme and a semiimplicit scheme similar to one proposed by McPherson (1971).

Halberstam, I.↗
NASA NTRS1975

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

Harris, J. E.↗
NASA NTRS1978

An efficient, direct finite difference method for computing sound propagation in arbitrarily shaped two-dimensional and axisymmetric ducts without flow

An efficient, direct finite difference method is presented for computing sound propagation in non-stepped two-dimensional and axisymmetric ducts of arbitrarily varying cross section without mean flow. The method is not restricted by axial variation of acoustic impedance of the duct wall linings. The non-uniform two-dimensional or axisymmetric duct is conformally mapped numerically into a rectangular or cylindrical computational domain using a new procedure based on a method of fast direct solution of the Cauchy-Riemann equations. The resulting Helmholtz equation in the computational domain is separable. The solution to the governing equation and boundary conditions is expressed as a linear combination of fundamental solutions. The fundamental solutions are computed only once for each duct shape by means of the fast direct cyclic reduction method for the discrete solution of separable elliptic equations. Numerical results for several examples are presented to show the applicability and efficiency of the method.

Chakravarthy, S.↗
NASA NTRS1980

A two-dimensional finite-difference solution for the transient thermal behavior of a tubular solar collector

A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique were analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

Lansing, F. L.↗
NASA NTRS1982

Finite difference methods for the solution of unsteady potential flows

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

Caradonna, F. X.↗
NASA NTRS1990

Finite-difference models of ordinary differential equations - Influence of denominator functions

This paper discusses the influence on the solutions of finite-difference schemes of using a variety of denominator functions in the discrete modeling of the derivative for any ordinary differential equation. The results obtained are a consequence of using a generalized definition of the first derivative. A particular example of the linear decay equation is used to illustrate in detail the various solution possibilities that can occur.

Mickens, Ronald E.↗
NASA NTRS1993

Dispersion-relation-preserving finite difference schemes for computational acoustics

Time-marching dispersion-relation-preserving (DRP) schemes can be constructed by optimizing the finite difference approximations of the space and time derivatives in wave number and frequency space. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. Close agreement with the exact solutions is obtained.

Tam, Christopher K. W.↗
NASA NTRS2000

COSIM: A Finite-Difference Computer Model to Predict Ternary Concentration Profiles Associated with Oxidation and Interdiffusion of Overlay-Coated Substrates

A finite-difference computer program (COSIM) has been written which models the one-dimensional, diffusional transport associated with high-temperature oxidation and interdiffusion of overlay-coated substrates. The program predicts concentration profiles for up to three elements in the coating and substrate after various oxidation exposures. Surface recession due to solute loss is also predicted. Ternary cross terms and concentration-dependent diffusion coefficients are taken into account. The program also incorporates a previously-developed oxide growth and spalling model to simulate either isothermal or cyclic oxidation exposures. In addition to predicting concentration profiles after various oxidation exposures, the program can also be used to predict coating fife based on a concentration dependent failure criterion (e.g., surface solute content drops to two percent). The computer code, written in an extension of FORTRAN 77, employs numerous subroutines to make the program flexible and easily modifiable to other coating oxidation problems.

Nesbitt, James A.↗