Search NASA⌕ Search

SEARCH · Search NASA

Results for “weak solutions”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

An incremental block-line-Gauss-Seidel method for the Navier-Stokes equations

A block-line-Gauss-Seidel (LGS) method is developed for solving the incompressible and compressible Navier-Stokes equations in two dimensions. The method requires only one block-tridiagonal solution process per iteration and is consequently faster per step than the linearized block-ADI methods. Results are presented for both incompressible and compressible separated flows: in all cases the proposed block-LGS method is more efficient than the block-ADI methods. Furthermore, for high Reynolds number weakly separated incompressible flow in a channel, which proved to be an impossible task for a block-ADI method, solutions have been obtained very efficiently by the new scheme.

Napolitano, M.↗
NASA NTRS1992

A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics

A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.

Iannelli, G. S.↗
NASA NTRS1983

A viscous shock-layer flowfield analysis by an explicit-implicit method

An implicit analogue of a widely used explicit method to external axisymmetric laminar flows with strong entropy gradients is extended. The details of the "numerics" of the implicit part are provided in a body oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analog may appeal to researchers for using it in the analysis of 3-D flow problems.

Gupta, R. M.↗
NASA NTRS1983

Viscous shock-layer flowfield analysis by an explicit-implicit method

The present work extends the recently reported implicit analogue of MacCormack's earlier widely-used explicit method to external axisymmetric laminar flows with strong entropy gradients. The details of the 'numerics' of the implicit part are provided in a body-oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analogue may appeal to researchers for using it in the analysis of three-dimensional flow problems.

Gupta, R. N.↗
NASA NTRS1990

Structure and evolution of small-amplitude intermediate shock waves

A simplified set of equations is derived that approximates the magnetohydrodynamic (MHD) Navier-Stokes equations for weakly nonlinear disturbances whose speeds are close to the MHD intermediate speed. Its shock structure solutions are then examined. The fast and slow shock solutions are uniquely specified by their Rankine-Hugoniot relations. However, the intermediate shock solutions, which are not unique, are characterized by the integral through the shock of the noncoplanar component of the magnetic field. For situations in which this integral is conserved, the Riemann problem is well defined and predicts the evolution of intermediate shocks. This analysis is substantiated by numerical computations.

Kennel, C. F.↗
NASA NTRS1975

Interaction between a shock wave and a turbulent boundary layer in transonic flow

Interaction between a shock wave and an unseparated turbulent boundary layer is considered. The method of matched asymptotic expansions is used, with solutions valid in the double limit as Reynolds number tends to infinity and Mach number tends to unity. The shock is weak enough that interaction effects can be considered as perturbations to the undisturbed flow; the case considered is that where the sonic line is near the outer edge of the boundary layer. It is shown that, with order estimates for Reynolds stress perturbations, the induced wall pressure distribution can be calculated using only the two outer interaction regions, independent of a specific closure condition and that this solution is in fact a turbulent free interaction solution. A detailed analysis of the inner regions, for which an eddy viscosity model for the Reynolds shear stress is used, provides a description of the variations in velocity, temperature and density near and at the wall.

Adamson, T. C., Jr.↗
NASA NTRS1992

Magnetic field decay in isolated neutron stars

Three mechanisms that promote the loss of magnetic flux from an isolated neutron star - Ohmic decay, ambipolar diffusion, and Hall drift - are investigated. Equations of motions are solved for charged particles in the presence of a magnetic field and a fixed background of neutrons, while allowing for the creation and destruction of particles by weak interactions. Although these equations apply to normal neutrons and protons, the present interpretations of their solutions are extended to cover cases of neutron superfluidity and proton superconductivity. The equations are manipulated to prove that, in the presence of a magnetic force, the charged particles cannot be simultaneously in magnetostatic equilibrium and chemical equilibrium with the neutrons. The application of the results to real neutron stars is discussed.

Goldreich, Peter↗
NASA NTRS2003

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

Dahl, Milo D.↗
NASA NTRS2004

Mineralogical Variations Among High Albedo E-Type Asteroids: Implications for Asteroid Igneous Processes

The link between the E-type asteroids and the enstatite achondrites (aubrites) was first proposed for the original E-asteroid, 44 Nysa. The association was based on the high albedos and the featureless spectra shared by the E-asteroids and the aubrites. Among the plausible geologic and meteoritic materials, only enstatite (the magnesium end-member of the pyroxene solid solution series) is sufficiently abundant to comprise asteroid-sized bodies. However, the presence of a weak 0.89 m absorption feature in the spectrum of 44 Nysa indicates that its pyroxene contains a small amount of Fe(2+) but still substantially more than any aubrite present in the meteorite collection. The original E-class was defined based on its high albedo and flat to slightly reddish spectrum. In the absence of albedo data, the E-type was degenerate with the M- and P-types, and together these were designated as X-types. Recently, a taxonomy has been proposed to identify E-types in the absence of albedo data. In this newer classification system three subdivisions of the X-type have been proposed, including Xc, Xe and Xk. Of nine albedo-defined E-types [d], this newer non-albedo based taxonomy produced the following classifications: X-1 asteroid; Xc-2 asteroids; Xe-5 asteroids; and Xk-1 asteroid. Although the Xe subtype includes the largest number of albedo-defined E-types, most of the remaining 24 Xe-types can be excluded based on their low measured IRAS albedos, ranging from 0.116 to 0.329, which are below the lower albedo limit of the E-class (0.34) and substantially below that of the lowest albedo an actual E-type asteroid (0.41). The present discussion will be limited to unambiguous E-type asteroids determined on albedo criteria.

Gaffey, Michael J.↗
NASA NTRS1980

Numerical solutions of transonic flows by parametric differentiation and integral equation techniques

The paper discusses results of an exploratory study of the advantages obtained by combining integral equation methods with the method of parametric differentiation in the treatment of transonic flow problems. In the proposed method, the nonlinear unsteady transonic flow equation for small perturbations is transformed into a linear equation by the use of the method of parametric differentiation. The linear equation is split into a pair of weakly coupled partial differential equations by writing the transformed perturbation potential as the sum of a steady component and an unsteady component. The solution of the steady equation as an integral equation is based on Ogana's treatment (1978). As a test case, the formulation is applied to predict the steady transonic flow over a nonlifting parabolic-arc airfoil.

Sivaneri, N. T.↗
NASA NTRS2004

The Role of Instability Waves in Predicting Jet Noise

There has been an ongoing debate about the role of linear instability waves in the prediction of jet noise. Parallel mean flow models, such as the one proposed by Lilley, usually neglect these waves because they cause the solution to become infinite. The resulting solution is then non-causal and can, therefore, be quite different from the true causal solution for the chaotic flows being considered here. The present paper solves the relevant acoustic equations for a non-parallel mean flow by using a vector Green s function approach and assuming the mean flow to be weakly non-parallel, i.e., assuming the spread rate to be small. It demonstrates that linear instability waves must be accounted for in order to construct a proper causal solution to the jet noise problem. . Recent experimental results (e.g., see Tam, Golebiowski, and Seiner,1996) show that the small angle spectra radiated by supersonic jets are quite different from those radiated at larger angles (say, at 90deg) and even exhibit dissimilar frequency scalings (i.e., they scale with Helmholtz number as opposed to Strouhal number). The present solution is (among other things )able to explain this rather puzzling experimental result.

Goldstein, M. E.↗
NASA NTRS1999

Directional Solidification of a Binary Alloy into a Cellular Convective Flow: Localized Morphologies

A steady, two dimensional cellular convection modifies the morphological instability of a binary alloy that undergoes directional solidification. When the convection wavelength is far longer than that of the morphological cells, the behavior of the moving front is described by a slow, spatial-temporal dynamics obtained through a multiple-scale analysis. The resulting system has a "parametric-excitation" structure in space, with complex parameters characterizing the interactions between flow, solute diffusion, and rejection. The convection stabilizes two dimensional disturbances oriented with the flow, but destabilizes three dimensional disturbances in general. When the flow is weak, the morphological instability behaves incommensurably to the flow wavelength, but becomes quantized and forced to fit into the flow-box as the flow gets stronger. At large flow magnitudes the instability is localized, confined in narrow envelopes with cells traveling with the flow. In this case the solutions are discrete eigenstates in an unbounded space. Their stability boundary and asymptotics are obtained by the WKB analysis.

Chen, Y.- J.↗
NASA NTRS1990

Injection efficiency of bound modes

Previous work on efficiency of light injection into the core of a fiber from a thin film and a bulk distribution of sources in the cladding have used the fields of a weakly guiding fiber. This approximation simplifies the analysis of the power efficiency by introducing universal values for the eigenvalues of different fibers with the same V-number, but cannot predict accurately the behavior of the injected light into a fiber with arbitrary differences in indices of refraction. The exact field solution was used in the expressions of the power efficiency, p sub eff, and its behavior as a function of the fiber parameter was analyzed. Weakly guiding results obtained previously are confirmed. However, P sub eff does not always increase with the V-number but with the difference in the indices of refraction, eta sub core-eta sub clad. For the bulk distribution it was found that P sub eff increases with the wavelength, lambda, and decreases with the fiber core radius, a, i.e., it decreases with the V-number. However, for the thin film, the P sub eff remains almost constant with lambda and the fiber core radius.

Egalon, Claudio Oliveira↗
NASA NTRS1994

Simultaneous solution for core magnetic field and fluid flow beneath an electrically conducting mantle

The effects of laterally homogeneous mantle electrical conductivity have been included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary and the subadjacent fluid motion; it also features Gauss' method for solving the nonlinear inverse problem associated with steady motional induction. The trade-off between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and fluid flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.

Voorhies, Goerte V.↗
NASA NTRS1975

Strong scintillations in astrophysics. I - The Markov approximation, its validity and application to angular broadening

The Markov approximation to the propagation of waves in an extended, irregular medium is discussed in an astrophysical context. A new derivation is presented which is simple and which shows that the assumption of Gaussian statistics used by previous authors is irrelevant. We discuss the relevance of the approximation and show that it may apply in many situations of interest, including interstellar scintillations of pulsar signals. The approximation does not require the assumption of weak scattering or Gaussian correlation functions. The Markov equation for the angular spectrum is particularly simple, and solutions are discussed for typical turbulence spectra. It is found that the equation for the angular spectrum is very nearly that used by previous authors, and the present discussion shows that these results are much more general than previously thought. A possible observational test for distinguishing between Gaussian and power-law interstellar density spectra is discussed.

Lee, L. C.↗
NASA NTRS1985

Numerical investigation of internal high-speed viscous flows using a parabolic technique

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Anderson, O. L.↗