Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical integration”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Unsteady supersonic aerodynamic theory by the method of potential gradient

A generalized solution of the hyperbolic wave equation has been derived. The method used has been further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals have been evaluated in closed form, while numerical integration methods are suggested for treating more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient because line integrations along the other two sides need only be considered. Furthermore, all the integrands vanish on the Mach cone and the need for determining the hyperbolic curves of intersection of the cone with the lifting surface is avoided. Generalized aerodynamic coefficients for three AGARD planforms have been calculated and compared with the available results.

Jones, W. P.↗
NASA NTRS1972

The influence of laser ranging on selenodetic control.

In this paper, a mathematical model is presented which can be used to perform an adjustment using laser distances to improve coordinates of points of the earth and on the moon. The observation equations are given and the orientation of the earth and the moon is defined in terms of three Eulerian angles. Parameters related to the orientation of the two bodies are the six initial conditions in each case, for the numerical integration of the three angles and their time derivatives. Numerical experiments were performed for the purpose of investigating the expected accuracies of the various parameters in the adjustment model under differing conditions. The results of the experiments indicate that the statistics for both the coordinates of points on earth and on the moon, and for the orientation parameters of the two bodies, are favorable.

Mueller, I. I.↗
NASA NTRS1973

Prior-to-failure extension of flaws under monotonic and pulsating loadings.

An equation governing the prior-to-failure crack propagation is proposed. For a rate-sensitive solid containing a two-dimensional crack and subject to the tensile mode of fracture the differential equations are integrated numerically for loads increasing monotonically in time. The resulting integral curves of load vs crack length and length vs time indicate that the growth of cracks in the subcritical range is strongly rate-dependent. The fatigue growth, viewed as a sequence of slow growth periods, is simulated on an EAI 380 analog computer. The fourth-power law proposed by Paris is confirmed only within certain range of high-cycle fatigue propagation and for a rate-insensitive solid. Otherwise, i.e., for a more pronounced rate dependence induced by viscosity of a solid and/or in the proximity of the final instability point, the growth is markedly enhanced.

Wnuk, M. P.↗
NASA NTRS1981

Sound diffraction around screens and wedges for arbitrary point source locations

A development is presented for the Green's function for a point source in the vicinity of a rigid wedge. The diffraction contributions to the Green's function for arbitrary source and listener location is expressed in a form which can be readily evaluated using the Laguerre technique for numerical integration. The present approach offers the advantages of efficient numerical evaluation and of relatively straightforward reduction to well-known analytical approximations in limiting cases. Comparisons with previously obtained experimental and numerical results obtained by Ambaud and Bergassoli (1972) are presented. The comparison with the experimental results is excellent; the advantages of the present numerical technique, vis a vis that of Ambaud and Bergassoli, are pointed out.

Hadden, W. J., Jr.↗
NASA NTRS1990

Downdating a time-varying square root information filter

A new method to efficiently downdate an estimate and covariance generated by a discrete time Square Root Information Filter (SRIF) is presented. The method combines the QR factor downdating algorithm of Gill and the decentralized SRIF algorithm of Bierman. Efficient removal of either measurements or a priori information is possible without loss of numerical integrity. Moreover, the method includes features for detecting potential numerical degradation. Performance on a 300 parameter system with 5800 data points shows that the method can be used in real time and hence is a promising tool for interactive data analysis. Additionally, updating a time-varying SRIF filter with either additional measurements or a priori information proceeds analogously.

Muellerschoen, Ronald J.↗
NASA NTRS1991

Solution of the Navier-Stokes equations for a driven cavity

The flow field in a lid driven cavity is determined by integration of the incompressible Navier-Stokes equations. The numerical integration is accomplished via an operator splitting method known as the theta-scheme. This splitting separates the problem into the solution of a quasi-stokes problem and a nonlinear convection problem. Some details of solution methods used for the two subproblems and results obtained for the driven cavity are described. The schemes developed for the quasi-Stokes problem are more advanced at this stage than those for the nonlinear problem. However, the approaches used for both parts are outlined. As a model problem, a two dimensional square cavity with sides of unit length and a lid moving with unit velocity from left to right is considered. The Navier-Stokes equations are discretized in space on a uniform staggered or MAC mesh. The time discretization is accomplished via the theta-scheme.

Semeraro, B. D.↗
NASA NTRS2002

Designing Adaptive Low Dissipative High Order Schemes

Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.

Yee, H. C.↗
NASA NTRS1982

A numerical method for the dynamics of non-spherical cavitation bubbles

A boundary integral numerical method for the dynamics of nonspherical cavitation bubbles in inviscid incompressible liquids is described. Only surface values of the velocity potential and its first derivatives are involved. The problem of solving the Laplace equation in the entire domain occupied by the liquid is thus avoided. The collapse of a bubble in the vicinity of a solid wall and the collapse of three bubbles with collinear centers are considered.

Lucca, G.↗
DOE OSTI2021

Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations

Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data as well as particle insertions are avoided. Furthermore, no simulations at “uninteresting” state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semigrand canonical ensemble (NPT Δ μ ). We describe this Monte Carlo-based Clapeyron integration method, including its basic physical and numerical principles, our extension to electron-ion plasmas, and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense carbon-oxygen plasmas under conditions relevant for the cores of white dwarf stars and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1977

On the improvement of deconvolution with digitized data using a Runge-Kutta integration scheme

A relatively simple change in the treatment of the input function in numerical integration of high-order differential equations by Runge-Kutta methods provides substantial improvements in accuracy, particularly when the forcing function is in digitized form. The Runge-Kutta-Gill coefficients are modified to incorporate the changes; with pulse-type excitations, improvements on the order of 2 to 50 times greater accuracy are demonstrated.

Houghton, J. R.↗
NASA NTRS1971

Prior-to-failure extension of flaws under monotonic and pulsating loadings: Inelastic fatigue

An equation governing the prior to failure crack propagation is proposed. For a rate-sensitive solid containing two-dimensional crack and subject to the tensile mode of fracture, the differential equations are integrated numerically for the loads increasing monotonically in time. The resulting integral curves sigma = sigma(l) and l = l(t), i.e. load vs. crack length and length vs. time, indicate that the growth of cracks in the subcritical range is strongly rate dependent. The fatigue growth, viewed as a sequence of slow growth periods, is simulated on an EAI 380 analogue computer. The fourth power law proposed by Paris is confirmed only within a certain range of high-cycle fatigue propagation and for a rate-insensitive solid. For a more pronounced rate dependency, induced by the viscosity of a solid and/or in the proximity of the final instability point, the growth is markedly enhanced.

Wnuk, M. P.↗
NASA NTRS1991

IMP: A performance code

IMP (Integrated Mission Program) is a simulation language and code used to model present and future Earth, Moon, or Mars missions. The profile is user controlled through selection from a large menu of events and maneuvers. A Fehlberg 7/13 Runge-Kutta integrator with error and step size control is used to numerically integrate the differential equations of motion (DEQ) of three spacecraft, a main, a target, and an observer. Through selection, the DEQ's include guided thrust, oblate gravity, atmosphere drag, solar pressure, and Moon gravity effects. Guide parameters for thrust events and performance parameters of velocity changes (Delta-V) and propellant usage (maximum of five systems) are developed as needed. Print, plot, summary, and debug files are output.

Dauro, Vincent A., Sr.↗
NASA NTRS1994

Semiclassical Study of the Wave Vector Dependence of the Interband Impact Ionization Rate in Bulk Silicon

We present calculations of the interband impact ionization rate calculated using a wave vector dependent (k-dependent) semiclassical formulation of the transition rate. The transition rate is determined using Fermi's golden rule from a two-body screened Coulomb interaction assuming energy and momentum conservation. The transition rate is calculated for the first two conduction bands of silicon by numerically integrating over the full Brillouin zone. The overlap integrals in the expression for the transition rate are determined numerically using a 15 band k-p calculation. It is found that the transition rate depends strongly on the initiating electron wave vector (k vector) and that the transition rate is greatest for electrons originating within the second conduction band than the first conduction band. An ensemble Monte Carlo simulation, which includes the numerically determined ionization transition rate as well as the full details of the first two conduction bands, is used to calculate the total impact ionization rate in bulk silicon. Good agreement with the experimentally determined electron ionization rate data is obtained.

Wang, Yang↗
NASA NTRS2003

The trajectory of a photon : general relativity light time delay

In this paper, a formula is developed for the total one-way transit time of a photon in the coordinate time of General Relativity. A bending term is identified that contributes about 10 ns to the transit time of a photon that grazes the Sun and is not generally included in other formula in the literature. The results are verified by performing numerical integration of the equations of motion for a photon. A numerical photon ephemeris is computed and compared with the analytic formula.

Tury, Slam G.↗