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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

An efficient numerical method for solving the time-dependent compressible Navier-Stokes equations at high Reynolds number

A fine-mesh method incorporating two new operators, which drastically reduces the computation time, has been developed for solving the time-dependent Navier-Stokes equations at flight Reynolds numbers. The approach time-splits the equations into a hyperbolic part and a parabolic part, solves the hyperbolic part by a new explicit numerical method based on characteristics theory, and solves the parabolic part by a new efficient implicit parabolic method. The method has reduced the computation time by one and two orders of magnitude from that required previously to solve for the interaction of a shock wave with a boundary layer on a flat plate.

Maccormack, R. W.↗
NASA NTRS1979

Utility of a finite element solution algorithm for initial-value problems

The Galerkin criterion within a finite element Weighted Residuals formulation is employed to establish an implicit solution algorithm for an initial-value partial differential equation. Numerical solutions of a transient parabolic and a hyperbolic equation, obtained using linear, quadratic and two cubic finite element basis functions, are employed to quantize accuracy and confirm and refine theoretical convergence rate estimates. The linear basis algorithm for the hyperbolic equation displays excellent accuracy on a coarse computational grid and a high-order convergence rate with discretization refinement. Good accuracy and a strong convergence rate in surface flux are determined for a nonhomogeneous Neumann boundary constraint applied to a parabolic equation. The results amply demonstrate the impact of the nondiagonal finite element initial-value matrix structure on solution accuracy and/or convergence rate.

Baker, A. J.↗
NASA NTRS1978

On the construction and application of implicit factored schemes for conservation laws

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Warming, R. F.↗
NASA NTRS1981

The stability of pseudospectral-Chebyshev methods

The pseudospectral-Chebyshev methods are shown to be convergent in variable coefficient problems and, in some cases, hyperbolic problems. The analysis demonstrates that the rate of convergence is greater for finite difference methods or the finite element method. For a single first-order hyperbolic equation, the method is seen as remaining stable even when the coefficient changes sign, although in this case it is specified that care must be taken to have adequate spatial resolution. It is noted that this fact, combined with the fact that collocation methods are easy to apply in the nonlinear case, shows that the pseudospectral method is in general preferable to the Galerkin or Tau methods.

Gottlieb, D.↗
NASA NTRS1981

Trends in unmanned planetary entry systems

Entry systems used in unmanned planetary exploration are discussed in terms of future missions and more complex demands made upon the design configurations of orbiters and atmospheric space probes. The presently on-going Galileo project involving a Jupiter orbiter and a probe of the Jovian atmosphere is mentioned, and the difficult entry requirements at a velocity of 48 km/sec and an angle of minus seven to minus 10 degrees into an atmosphere composed largely of hydrogen, are described. Re-entry parameters determined by the respective entry environment, type of entry approach (hyperbolic or elliptical orbit) entry velocity, and guidance technology are given attention. Aerobraking, involving relatively slow circularization of an initial elliptical orbit by repeated passes through the atmosphere, is investigated. Aerocapture, by which vehicles using controlled flight paths through the atmosphere, can go directly from a hyperbolic flyby trajectory to low circular orbit is described. Major attractions of aerobraking and aerocapture are analyzed in terms of modest technology needs and relatively small impact on spacecraft design.

French, J. R.↗
NASA NTRS1982

Computation of three-dimensional inviscid flow over hypersonic missile configurations using the GIM code

A three-dimensional computational technique was used to obtain flowfield solutions to the Euler equations over selected hypersonic missile configurations. The General Interpolants Method (GIM) computer code was used with interpolation functions in an algebraic approach to generate a discrete computational grid for each configuration. The spatial marching version of the GIM code, which treats the parabolized Navier-Stokes (PNS) equations or the Euler equations with a shock capturing, 'MacCormack-like' scheme, was used to advance the solution hyperbolically over each configuration. The inviscid flowfield solutions over the two three-dimensional missile configurations, calculated using the GIM hyperbolic scheme, are presented here. The flow field over a wing/body configuration at zero degree angle of attack is presented. Flow over the fuselage of a tactical missile, termed the TAME 10, at both zero degree and 7.5 degree angles of attack is presented. In addition, an inviscid, two-dimensional analysis of an inlet configuration designed to mount on the TAME 10 is included. Contour maps of velocity and pressure are included for each configuration. Comparison of calculation and data show good agreement.

Xiques, K. E.↗
NASA NTRS1983

Application of second-order-accurate Total Variation Diminishing (TVD) schemes to the Euler equations in general geometries

A one-parameter family of explicit and implicit second-order-accurate, entropy satisfying, total variation diminishing (TVD) schemes was developed by Harten. These TVD schemes were the property of not generating spurious oscillations for one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. Application of these methods to one- and two-dimensional fluid flows containing shocks (in Cartesian coordinates) yields highly accurate nonoscillatory numerical solutions. The goal of this work is to expand these methods to the multidimensional Euler equations in generalized coordinate systems. Some numerical results of shock waves impinging on cylindrical bodies are compared with MacCormack's method.

Yee, H. C.↗
NASA NTRS1983

On the symmetric form of systems of conservation laws with entropy

The present investigation has the objective to review the general structure of system of conservation laws with entropy, giving particular attention to a presentation of symmetric formulations of the equations of gas dynamics. Systems of hyperbolic conservation laws are considered, taking into account the case in which a system of equations is symmetric hyperbolic, questions of symmetrization, and entropy functions. The Euler equations for a polytropic gas in conservation form are considered. The symmetric form retains the conservation properties of the equations. Weak solutions remain, therefore, unchanged. Of particular computational interest is the possibility of using the symmetric form.

Harten, A.↗
NASA NTRS1982

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

Larson, V. H.↗
NASA NTRS1985

Post-instability behavior of solids

The necessity of model reformulation in elasticity results from the failure of hyperbolicity of the governing equations of motion for classical models. The reformulation is based upon the introduction of additional kinematical microstructures in the form of multivalued displacement and velocity field (or fractal functions) which are generated by the mechanism of the instability. The small scale motions describing this microstructure interact with the original large scale motion and restore the hyperbolicity of new governing equations of motion. The applications of the reformulated models to the problem of vibrational control and impact energy absorption are discussed.

Zak, M.↗
NASA NTRS1986

Circulating transportation orbits between earth and Mars

This paper describes the basic characteristics of circulating (cyclical) orbit design as applied to round-trip transportation of crew and materials between earth and Mars in support of a sustained manned Mars Surface Base. The two main types of nonstopover circulating trajectories are the socalled VISIT orbits and the Up/Down Escalator orbits. Access to the large transportation facilities placed in these orbits is by way of taxi vehicles using hyperbolic rendezvous techniques during the successive encounters with earth and Mars. Specific examples of real trajectory data are presented in explanation of flight times, encounter frequency, hyperbolic velocities, closest approach distances, and Delta V maneuver requirements in both interplanetary and planetocentric space.

Friedlander, A. L.↗
NASA NTRS1987

Development and application of unified algorithms for problems in computational science

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.

Shankar, Vijaya↗
NASA NTRS1988

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, Jeffrey M.↗
NASA NTRS1989

A class of high resolution explicit and implicit shock-capturing methods

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Yee, H. C.↗
NASA NTRS1990

Numerical methods for systems of conservation laws of mixed type using flux splitting

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

Shu, Chi-Wang↗
NASA NTRS1989

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, J. M.↗
NASA NTRS1990

Optimal trajectories based on linear equations

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

Carter, Thomas E.↗
NASA NTRS1991

Parametric entry corridors for lunar/Mars aerocapture missions

Parametric atmospheric entry corridor data are presented for Earth and Mars aerocapture. Parameter ranges were dictated by the range of mission designs currently envisioned as possibilities for the Human Exploration Initiative (HEI). This data, while not providing a means for exhaustive evaluation of aerocapture performance, should prove to be a useful aid for preliminary mission design and evaluation. Entry corridors are expressed as ranges of allowable vacuum periapse altitude of the planetary approach hyperbolic orbit, with chart provided for conversion to an approximate flight path angle corridor at entry interface (125 km altitude). The corridor boundaries are defined by open-loop aerocapture trajectories which satisfy boundary constraints while utilizing the full aerodynamic control capability of the vehicle (i.e., full lift-up or full lift-down). Parameters examined were limited to those of greatest importance from an aerocapture performance standpoint, including the approach orbit hyperbolic excess velocity, the vehicle lift to drag ratio, maximum aerodynamic load factor limit, and the apoapse of the target orbit. The impact of the atmospheric density bias uncertainties are also included. The corridor data is presented in graphical format, and examples of the utilization of these graphs for mission design and evaluation are included.

Ling, Lisa M.↗