Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical differentiation”

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 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Contribution to the theory of tidal oscillations of an elastic earth. External tidal potential

The differential equations of the tidal oscillations of the earth were established under the assumption that the interior of the earth is laterally inhomogeneous. The theory was developed using vectorial and dyadic symbolism to shorten the exposition and to reduce the differential equations to a symmetric form convenient for programming and for numerical integration. The formation of tidal buldges on the surfaces of discontinuity and the changes in the internal density produce small periodic variations in the exterior geopotential which are reflected in the motion of artificial satellites. The analoques of Love elastic parameters in the expansion of exterior tidal potential reflect the asymmetric and inhomogeneous structure of the interior of the earth.

Musen, P.↗
NASA NTRS1974

Geothermal reservoir simulation

The prediction of long-term geothermal reservoir performance and the environmental impact of exploiting this resource are two important problems associated with the utilization of geothermal energy for power production. Our research effort addresses these problems through numerical simulation. Computer codes based on the solution of partial-differential equations using finite-element techniques are being prepared to simulate multiphase energy transport, energy transport in fractured porous reservoirs, well bore phenomena, and subsidence.

Mercer, J. W., Jr.↗
NASA NTRS1978

A three-dimensional model of corotating streams in the solar wind. 1: Theoretical foundations

The theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions (3-D) is discussed. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 solar radii where the flow is supersonic) is approximately described by the nonlinear, single fluid, polytropic (magneto-) hydrodynamic equations. Efficient numerical techniques for solving this complex system of coupled, hyperbolic partial differential equations are outlined. The formulation is inviscid and nonmagnetic, but methods allow for the potential inclusion of both features with only modest modifications. One simple, highly idealized, hydrodynamic model stream is examined to illustrate the fundamental processes involved in the 3-D dynamics of stream evolution. Spatial variations in the rotational stream interaction mechanism were found to produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction.

Pizzo, V. J.↗
NASA NTRS1978

Calculation of electrostatic fields in periodic structures of complex shape

A universal algorithm is presented for calculating electrostatic fields in an infinite periodic structure consisting of electrodes of arbitrary shape which are located in mirror-symmetrical manner along the axis of electron-beam propagation. The method is based on the theory of R-functions, and the differential operators which are derived on the basis of the functions. Numerical results are presented and the accuracy of the results is examined.

Kravchenko, V. F.↗
NASA NTRS1979

Analytical modeling of flash-back phenomena

To understand the flame flash-back phenomena more extensively, an analytical model was formed and a numerical program was written and tested to solve the set of differential equations describing the model. Results show that under a given set of conditions flame propagates in the boundary layer on a flat plate when the free stream is at or below 1.8 m/s.

Feng, C. C.↗
NASA NTRS1981

Multigrid simulation of asymptotic curved-duct flows using a semi-implicit numerical technique

Asymptotic flows inside curved ducts of rectangular as well as polar cross section are analyzed using the Navier-Stokes equations in terms of the axial velocity and vorticity and the cross-flow stream function. Numerical solutions of the three second-order coupled elliptic partial differential equations governing this flow are obtained efficiently using the coupled alternating-direction implicit (ADI) method as well as the multigrid strongly-implicit (SI) scheme. For the flow configuration studied, the ADI method is found to be more sensitive to the time steps used than is the SI scheme. Use of the multigrid-coupled-strongly-implicit (MG-SI) scheme makes it possible to efficiently obtain fine-grid solutions for configurations having strong secondary flow. It is shown that, for this asymptotic curved-duct flow, the similarity parameter of significance is the Dean's number K rather than the Reynolds number Re. Results are obtained for curved ducts with square cross sections for K up to 900, which here corresponds to Re = 9,000 for this internal flow configuration.

Ghia, K. N.↗
NASA NTRS1983

N-person differential games. Part 2: The penalty method

The equilibrium strategy for N-person differential games can be found by studying a min-max problem subject to differential systems constraints. The differential constraints are penalized and finite elements are used to compute numerical solutions. Convergence proof and error estimates are given. Numerical results are also included and compared with those obtained by the dual method.

Chen, G.↗
NASA NTRS1983

Study of asymptotic incompressible flow in curved ducts using a multi-grid technique

Asymptotic flows inside curved ducts of rectangular as well as polar cross sections have been analyzed using the Navier-Stokes equations in terms of the axial velocity and vorticity and the cross-flow stream function. Numerical solutions of the three second-order coupled elliptic partial differential equations governing this flow have been obtained using the multi-grid-SI scheme, to determine fine-grid results for configurations with strong secondary flow.

Ghia, K. N.↗
NASA NTRS1986

Electron-positron pair production by ultrarelativistic electrons in a soft photon field

The fully differential cross section for photon-electron pair production is integrated numerically over phase space. Results are obtained for the astrophysically interesting case in which the interaction between an ultrarelativistic electron and a soft photon results in electron-positron pair production. The positron spectrum is a function of the energies of both the photon and the electron, as well as the angle of interaction. It is found that the energy at which the positron distribution peaks is inversely proportional to the photon energy and independent of the electron energy. The positron spectrum is integrated once more over initial electron energies for a power-law energy distribution of primary electrons. The same procedure is repeated for the recoil particle; it is shown that the peak of the recoil energy distribution depends linearly on the energy of the primary electron. Finally, semianalytical expressions are obtained for the energy losses of the primary electrons.

Mastichiadis, A.↗
NASA NTRS1986

Preconditioned conjugate residual methods for the solution of spectral equations

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Wong, Y. S.↗
NASA NTRS1984

Effect of particulate thermophoresis in reducing the fouling rate advantages of effusion-cooling

To predict small-particle diffusional mass transfer (deposition), including particle thermophoresis, transpiration cooling, and variable properties, the coupled ordinary differential equations governing self-similar laminar boundary layers are solved numerically. Under typical combustion turbine conditions, although diffusional deposition rates can be dramatically reduced by transpiration cooling (e.g., by some 5-decades for mainstream submicron particles corresponding to a Schmidt number of about 100 and a wall transpiration-cooled to Tw/Te = 0.8), actual deposition rate reductions will be smaller than previously expected (by about 1 decade for particles with Sc of about 100), owing to thermophoretic particle drift caused by the colder wall. Such microdroplets, small enough to behave like heavy molecules in combustion systems, are often important because they can cause adherence of the much larger ash particles which inertially impact on the same surface.

Gokoglu, S. A.↗
NASA NTRS1991

Choice of velocity variables for complex flow computation

The issue of adopting the velocity components as dependent velocity variables for the Navier-Stokes flow computations is investigated. The viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form. With the use of Cartesian velocity vector, the momentum equations in curvilinear coordinates can retain the full conservation-law form and satisfy the physical conservation laws. With the curvilinear velocity components, source terms appear in differential equations and hence the full conservation law form can not be retained. In discrete expressions, algorithms based on the Cartesian components can satisfy the geometric conservation-law form for convection terms but not for viscous terms; those based on the curvilinear components, on the other hand, cannot satisfy the geometric conservation-law form for either convection or viscous terms. Several flow solutions for domain with 90 and 360 degree turnings are presented to illustrate the issues of using the Cartesian velocity components and the staggered grid arrangement.

Shyy, W.↗
NASA NTRS1991

Exotic containers for capillary surfaces

This paper discusses 'exotic' rotationally symmetric containers that admit an entire continuum of distinct equilibrium capillary free surfaces. The paper extends earlier work to a larger class of parameters and clarifies and simplifies the governing differential equations, while expressing them in a parametric form appropriate for numerical integration. A unified presentation suitable for both zero and nonzero gravity is given. Solutions for the container shapes are depicted graphically along with members of the free-surface continuum, and comments are given concerning possible physical experiments.

Concus, Paul↗
NASA NTRS1993

The use of linked lists in the simulation of controller-structure interaction

An algorithm for the computer simulation of large space structures under active control is considered. Linked lists are used in a matrix data structure to implement the trapezoidal rule on system differential equations. The use of the trapezoidal rule ensures that the numerical stability is equivalent to the system stability, which is essential for this type of simulation. The sparsity of the system matrices is exploited by the linked lists, and the algorithm efficiently steps through the lists in an orderly fashion. Results of simulations on a NASA large space structure experiment are reported.

Quan, R.↗
NASA NTRS1993

The use of linked lists in the simulation of controller-structure interaction

An algorithm for the computer simulation of large space structures under active control is considered. Linked lists are used in a matrix data structure to implement the trapezoidal rule on the system differential equations. The use of the trapezoidal rule ensures that the numerical stability is equivalent to the system stability, which is essential for this type of simulation. The sparsity of the system matrices is exploited by the linked lists, and the algorithm efficiently steps through the lists in an orderly fashion. Results of simulations on a NASA large space structure experiment are reported.

Quan, Ralph↗
NASA NTRS1995

Investigation of dispersion-relation-preserving scheme and spectral analysis methods for acoustic waves

Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.

Vanel, Florence O.↗
NASA NTRS1998

Investigation of Vibrational Control of the Bridgman Crystal Growth Technique

The objectives are: Conduct a parametric theoretical and numerical investigation of vibro-convective buoyancy-driven flow in differentially heated cylindrical containers. Investigate buoyant vibro-convective transport regimes in Bridgman-type systems with a focus on the use of vibration to suppress, or control, convection in order to achieve transport control during crystal growth. Assess the feasibility of vibro-convective control as a means of offsetting "g-jitter" effects under microgravity conditions, Exchange information with the experimental group at the General Physics Institute (GPI) of the Russian Academy of Science who are undertaking a complementary experimental program.

Fedoseyev, Alexandre I.↗