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Results for “High-order methods”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Direct simulations of turbulent flow using finite-difference schemes

A high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow. The methods used include a kinetic energy conserving central difference scheme and an upwind difference scheme. The methods are evaluated in test cases for the evolution of small-amplitude disturbances and fully developed turbulent channel flow. It is suggested that the finite-difference approach can be applied to complex geometries more easilty than highly accurate spectral methods. It is concluded that the upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries.

Rai, Man Mohan↗
NASA NTRS1989

Numerical solutions of forward-flight rotor flow using an upwind method

A finite-volume upwind algorithm for solving the 3-D Euler equations with a moving grid has been developed for computing helicopter forward-flight rotor flows. The computed pressure distributions and shock positions of high-speed rotor flow are compared with various experimental data as well as with other numerical results, and the agreement is encouraging. A comparison of quasi-steady solutions with unsteady solutions reveals that when a shock occurs in the flowfield, the assumption of quasi-steady flow may fail due to the time-lag of the shock motion. Similarly, three-dimensional effects cannot be neglected. Sufficient subiterations for each time step are required to avoid numerical lag effects in using the present method. The redistribution of the residual due to the coordinate transformation is discussed. For high-order MUSCL-type schemes, a coordinate-independent solution can be obtained by interpolating primitive variables.

Chen, C. L.↗
NASA NTRS1975

Stabilization of large-scale systems - A spinning flexible spacecraft

Stabilization of high-order constant systems by multilevel control is proposed in the framework of the decomposition-aggregation method for stability analysis of large-scale systems. An 11-order linear model of a spinning flexible spacecraft is stabilized by the method using both the passive and the active stabilization devices. The method can take advantage of the special structural features of the model to provide the best estimate of the stability region for an important parameter which couples the wobble and the spin motion of the spacecraft.

Siljak, D. D.↗
NASA NTRS1986

Uniformly high order accurate essentially non-oscillatory schemes 3

In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

Harten, A.↗
NASA NTRS1990

Supersonic aerodynamic characteristics of a Mach 3 high-speed civil transport configuration

The NASA-Langley AST31 high-speed civil transport (HSCT) configuration, a blended wing/fuselage concept scaled for 250-passenger carriage over 6500 nmi, has been subjected to both CFD and wind tunnel tests; the wind tunnel tests were conducted in the Mach 1.6-3.6 range. The inability of the linear theory method to accurately predict stability levels as well as nonlinear pitching moment characteristics demonstrates the need to undertake high-order analyses as early in the design process as possible. An HSCT laminar flow capability experimental study was conducted in order to simulate 50-percent laminar flow conditions, and thereby ascertain the difference in drag relative to fully turbulent conditions.

Covell, Peter F.↗
NASA NTRS1988

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

Buell, Jeffrey C.↗
NASA NTRS1984

A spectral element method for fluid dynamics - Laminar flow in a channel expansion

A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

Patera, A. T.↗
NASA NTRS1990

Flux-difference split scheme for turbulent transport equations

This paper describes a high accuracy upwind method to solve the mean compressible flow equations closed with two-equation turbulence models. A flux-difference splitting scheme is developed to compute the flowfield without introducing oscillations into the solution. A high-order accuracy scheme is used to predict both the mean flow variables and the turbulence variables. Results comparing two different two-equation turbulence models are presented for supersonic flow over a flat plate and a compressible, free shear-layer. The non-oscillatory behavior of the upwind scheme is demonstrated on the free shear-layer.

Morrison, J. H.↗
NASA NTRS1989

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially non-oscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗
NASA NTRS1987

Application of a sensitivity analysis technique to high-order digital flight control systems

A sensitivity analysis technique for multiloop flight control systems is studied. This technique uses the scaled singular values of the return difference matrix as a measure of the relative stability of a control system. It then uses the gradients of these singular values with respect to system and controller parameters to judge sensitivity. The sensitivity analysis technique is first reviewed; then it is extended to include digital systems, through the derivation of singular-value gradient equations. Gradients with respect to parameters which do not appear explicitly as control-system matrix elements are also derived, so that high-order systems can be studied. A complete review of the integrated technique is given by way of a simple example: the inverted pendulum problem. The technique is then demonstrated on the X-29 control laws. Results show linear models of real systems can be analyzed by this sensitivity technique, if it is applied with care. A computer program called SVA was written to accomplish the singular-value sensitivity analysis techniques. Thus computational methods and considerations form an integral part of many of the discussions. A user's guide to the program is included. The SVA is a fully public domain program, running on the NASA/Dryden Elxsi computer.

Paduano, James D.↗
NASA NTRS1981

The gravity field in the central Pacific from satellite-to-satellite tracking

Satellite-to-satellite Doppler tracking between the ATS 6 and the GEOS 3 spacecraft was used to measure the high-degree and high-order gravity field over an 80-deg region in the central Pacific Ocean. Forty passes of GEOS 3/ATS 6 Doppler data have been analyzed. The precision of these range rate data is about 0.3 mm/s, and the line-of-sight gravity anomalies recovered from these data have a precision of about 0.2 mGal at the GEOS 3 altitude of about 840 km. In general, the agreement between the SST-derived map and the conventional GEM method and an altimeter-derived geoid is good. Eight significant positive gravity anomalies were exposed in the central Pacific. Generally speaking, the anomalies form a roughly east-west pattern of alternating sign in the central region, and near the East Pacific they strike about north and south.

Marsh, J. G.↗
NASA NTRS1970

Discrete control of linear distributed systems with application to the deformable primary mirror of a large orbiting telescope

One of the more significant technological problems associated with the orbital operation of large astronomical telescope's is the fabrication and maintenance of the primary mirror surface to the tolerance required for diffraction-limited performance. An interesting approach to the solution of this problem involves continuously measuring and automatically correcting the optical surface of a thin deformable mirror by means of discrete actuators located on its rear surface: The realization of diffraction-limited performance from a telescope in space by this method rests on the ability of the designer to achieve extremely accurate control of a highly complex, interacting, multivariable system. This paper presents the results of a detailed study of the discrete control of linear distributed systems with specific application to the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory. The problem of controlling the distributed plant is treated by employing modal techniques to represent variations in the optical figure. Distortion of the mirror surface, which arises primarily from thermal gradients, is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each displacement actuator is in series with a spring attached to the mirror by means of a pad intentionally introduced to restrict the excitation of high-order modes. Control is then exerted over a finite number (equal.to the number of actuators) of the most significant modes. Through the application of the modal expansion technique the mirror equation of motion is transformed tb a set of uncoupled, linear, time-invariant, ordinary differential equations. The desired dynamic response and static accuracy may then be achieved by the application of classical single-variable design techniques. The formulation of a quadratic performance index which incorporates a measure of image quality permits determination of the trade-off between the-number of actuators and optical purity. A criterion for defining actuator placement and pad size is presented which minimizes the tendency of the controller to excite the unmonitored modes.

Jeremiah F Creedon↗
NASA NTRS1975

High-order numerical solutions using cubic splines

The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.

Rubin, S. G.↗
NASA NTRS1980

The unique determination of density from high-order potentials

The existence of higher-order potentials is postulated, and that the density function can be determined from this set of potentials is demonstrated. Moreover, it is shown that there is a one-to-one correspondence between such potentials and the density function, provided it is continuous. Finally, it is noted that this demonstration includes a method of constructing the density function from the set of potentials as well as indicating how to approximate the density from incomplete knowledge of the potentials.

Johnson, G. G.↗
NASA NTRS1986

A spectral multi-domain technique with application to generalized curvilinear coordinates

Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic and fluid mechanic problems. The high order accuracy and resolution shown by these methods allows one to obtain engineering accuracy solutions on coarse meshes, or alternatively, to obtain solutions with very small error. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be preserved. Additionally even smooth stretching transformations can decrease the accuracy of a spectral method, if the stretching is severe. A further difficulty with spectral methods was in their implementation on parallel processing computers, where efficient spectral algorithms were lacking. The above restrictions are overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of the mesh spacing between regions to be several orders of magnitude higher than allowable in a single domain. Such stretchings would be required to resolve the thin viscous region in an external aerodynamic problem. Adjoining regions are interfaced by enforcing a global flux balance which preserves high-order continuity of the solution, regardless of the type of the equations being solved.

Macaraeg, M. G.↗
NASA NTRS1986

Minimum-fuel control of high-order systems

The minimum-fuel control problem is of special interest in various space systems. To date, solutions of minimum-fuel control problems have been carried out for relatively low-order systems. Space structures, however, are generally characterized by a large number of degrees of freedom, so that minimum-fuel control of such systems requires a new approach. In the independent modal-space control (IMSC) method, the control laws are designed in the modal space for each mode independently. The minimum-fuel problem reduces to that of a set of independent second-order systems, so that minimum-fuel control is possible. This paper shows how the IMSC method can be used to control a space structure with a minimum amount of fuel. A numerical example is presented.

Shenhar, J.↗
NASA NTRS1987

Navier-Stokes simulations of blade-vortex interaction using high-order accurate upwind schemes

Conventional, spatially second-order-accurate, finite-difference schemes are much too dissipative for calculations involving vortices that travel large distances (relative to some measure of the size of the vortex). This study presents a fifth-order-accurate upwind-biased scheme that preserves vortex structure for much longer times than existing second-order-accurate central and upwind difference schemes. Vortex calculations demonstrating this aspect of the fifth-order scheme are also presented. The method is then applied to the blade-vortex interaction problem. Results for strong interactions wherein the vortex impinges directly on the airfoil or a shock associated with the airfoil are presented. None of these calculations required any modeling of the shape, size, and trajectory of the interacting vortex.

Rai, Man Mohan↗
NASA NTRS1989

A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

Liou, Meng-Sing↗