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Results for “Partial integral differential equations”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

A novel approach to the modelling and control of flexible robot arms

A general dynamic model of a two-link Euler-Bernoulli beam flexible robot arm is presented in the form of partial-differential-integral equations. Observations are made on important properties of the dynamic model. The resulting infinite-dimensional system is then input-output decoupled and partially linearized by a diffeomorphic state transformation and nonlinear state feedback. The local stability issue is addressed for a one-link flexible robot arm.

Ding, Xuru↗
NASA NTRS1977

Calculation of sheath and wake structure about a pillbox-shaped spacecraft in a flowing plasma

A computer program was used for studies of the disturbed zones around bodies in flowing plasmas, particularly spacecraft and their associated sheaths and wakes. The program solved a coupled Poisson-Vlasov system of nonlinear partial differential integral equations to obtain distributions of electric potential and ion and electron density about a finite length cylinder in a plasma flow at arbitrary ion Mach numbers. The approach was applicable to a larger range of parameters than other available approaches. In sample calculations, bodies up to 100 Debye lengths in radius were treated, that is, larger than any previously treated realistically. Applications were made to in-situ satellite experiments.

Parker, L. W.↗
NASA NTRS1994

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Abarbanel, Saul↗
NASA NTRS1982

Compressibility effects in turbulence modeling

Numerical turbulence modeling is discussed with attention given to fluid property variations caused by compressibility in an adiabatic flow. The models are considered in terms of integral quantities expressed by ordinary differential equations and by those formulated as partial differential equations. Compressibility corrections for both integral and partial differential methods are reviewed. Eddy-viscosity models are explored for their capability to characterize the mass-weighted Reynolds stress, which can be accounted for with primitive and/or mass-weighted variables. Compressible flow simulations are currently constrained to low Re and zero mean dilation. The effects of compressibility are defined in wave number space by resolving the Fourier transforms of the velocity vectors into components which are perpendicular and parallel to the wave number vector. Statistical correlations then permit obtaining a value for each contribution.

Rubesin, M. W.↗
NASA NTRS1989

A general dynamic model of flexible robot arms for control

Hamilton's principle is used to derive the dynamic model for a large class of flexible robot arms. The resultant dynamic model consists of a system of partial differential-integral equations and the dynamic boundary conditions associated with it. Some properties of the model are observed, and its application to control is discussed. This model represents an infinite-dimensional nonlinear dynamic system and yet can be turned into a finite-dimensional system that could be obtained by modal expansion, if it is desired. This provides more flexibility for control purposes as well as for the analysis of the system.

Ding, X.↗
NASA NTRS1990

Quadrature imposition of compatibility conditions in Chebyshev methods

This paper handles a problem encountered in the solution by way of Chebyshev spectral collocation discretization of the Poisson equation with homogeneous Neumann boundary conditions. When pseudospectral Chebyshev methodology is utilized to discretize the partial differential equation these integrals have to be approximated by an appropriate quadrature formula. The correct quadrature formula is developed for these problems, taking into account the degree of the polynomials involved. It is shown that this formula leads to a well-conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗
NASA NTRS1993

A dual reciprocal boundary element formulation for viscous flows

The advantages inherent in the boundary element method (BEM) for potential flows are exploited to solve viscous flow problems. The trick is the introduction of a so-called dual reciprocal technique in which the convective terms are represented by a global function whose unknown coefficients are determined by collocation. The approach, which is necessarily iterative, converts the governing partial differential equations into integral equations via the distribution of fictitious sources or dipoles of unknown strength on the boundary. These integral equations consist of two parts. The first is a boundary integral term, whose kernel is the unknown strength of the fictitious sources and the fundamental solution of a convection-free flow problem. The second part is a domain integral term whose kernel is the convective portion of the governing PDEs. The domain integration can be transformed to the boundary by using the dual reciprocal (DR) concept. The resulting formulation is a pure boundary integral computational process.

Lafe, Olu↗
NASA NTRS1974

Parametric study of relaminarization of turbulent boundary layers on nozzle walls

By means of comparisons between theoretical predictions and experimental data, the accuracy of a boundary procedure to predict the effect of large streamwise accelerations upon initially turbulent boundary layers is assessed. The boundary layer procedure is based upon simultaneous solution of the boundary layer partial differential equations and the integral turbulence kinetic energy equation. The results of the present investigation show the ability of the procedure to accurately predict properties of boundary layers subjected to large streamwise accelerations. The procedure is used to conduct a parametric study of the effect of free stream turbulence, heat transfer, Reynolds number, acceleration, and Mach number on boundary layers in supersonic nozzles to assist in the design of a quiet tunnel. Results of the investigation show that, even in the presence of moderate free-stream turbulence levels, the boundary layer in the approach section of the quiet tunnel nozzle relaminarizes and becomes thin enough to be removed by a small slot in the nozzle wall. Furthermore, the calculations indicate that it should be possible to maintain a laminar boundary layer for the entire length of the supersonic portion of the quiet tunnel nozzle.

Kreskovsky, J. P.↗
NASA NTRS1987

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗
NASA NTRS1990

A real-time approximate optimal guidance law for flight in a plane

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Feeley, Timothy S.↗
NASA NTRS1991

Distributed Minimal Residual (DMR) method for acceleration of iterative algorithms

A new method for enhancing the convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations was developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov subspace methods. The DMR method differs from the Krylov subspace methods by the fact that the iterative acceleration factors are different from equation to equation in the system. At the same time, the DMR method can be viewed as an incomplete Newton iteration method. The DMR method was applied to Euler equations of gas dynamics and incompressible Navier-Stokes equations. All numerical test cases were obtained using either explicit four stage Runge-Kutta or Euler implicit time integration. The formulation for the DMR method is general in nature and can be applied to explicit and implicit iterative algorithms for arbitrary systems of partial differential equations.

Lee, Seungsoo↗
NASA NTRS1995

The initial-value problem for viscous channel flows

Plane viscous channel flows are perturbed and the ensuing initial-value problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this works offers a means whereby completely arbitrary initial input can be specified without having to resort to eigenfunction expansions. The full temporal behavior, including both early time transients and the long time asymptotics, can be determined for any initial disturbance. Effects of three-dimensionality can be assessed. The bases for the analysis are: (a) linearization of the governing equations; (b) Fourier decomposition in the spanwise and streamwise directions of the flow; and (c) direct numerical integration of the resulting partial differential equations. All of the stability data that are known for such flows can be reproduced. Also, the optimal initial condition can be determined in a straight forward manner and such optimal conditions clearly reflect transient growth data that is easily determined by a rational choice of a basis for the initial conditions. Although there can be significant transient growth for subcritical values of the Reynolds number using this approach it does not appear possible that arbitrary initial conditions will lead to the exceptionally large transient amplitudes that have been determined by optimization of normal modes. The approach is general and can be applied to other classes of problems where only a finite discrete spectrum exists, such as the boundary layer for example.

Criminale, W. O.↗
NASA NTRS1968

Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Driskell, C. N., Jr.↗
NASA NTRS1990

Quadrature imposition of compatibility conditions in Chebyshev methods

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗