Search NASA⌕ Search

SEARCH · Search NASA

Results for “boundary value problem”

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 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Summer term 2018 work with IMC radiative transport in binary stochastic media

In the quest for new and improved methods to solve thermal radiation transport in stochastic media, this summer project was to characterize radation transport in a deterministic lattice problem that represents a real, binary stochastic media. A representative geometry for a binary stochastic media consisting of a cube of a high volume fraction media containing constant-diameter non-overlappying spheres randomly distributed within was run previously. Previous thermal radiation wave problems in binary stochastic media displayed three characteristic thermal energy deposition wavefronts in the following order, front of the spheres, bulk material, and the backs of the spheres. Several physical aspects of the representative geometry for a stochastic binary media using an optically thin background with optically thick spheres were analyzed. This analysis includes wave speed propagation using a one dimensional diffusion approximation, energy fluence transmission, and material energy deposition. The approaches to analysis included representing one sphere of the high opacity material in a diffusive background of the low opacity material, as well as repeating spheres in a column con guration with reflective boundary conditions to approximate a lattice. Additionally, both atomic mix and Levermore-Pomraning homogenization schemes were compared against the representative cube geometry as well as the sphere column lattice geometry. The wave speed analysis with a one dimensional Marshak diffusion wave was largely ineffective at determining an effective opacity value to which a problem could be homogenized, likely due to low mean free path resolution within the problem. However, the sphere column lattice geometry showed promising results for approximating the energy fluence transmitted through the problem domain. One concern with the sphere column lattice geometry indicated the high forward-bias effect of fluence reaching the problem boundary due to streaming paths around the spheres in the case of small mean free path resolution of the background material.

36 MATERIALS SCIENCE↗
NASA NTRS1973

Laminar film boiling on inclined isothermal flat plates.

Laminar film boiling from an inclined flat plate has been investigated analytically. Using the singular perturbation scheme, the complete set of Navier-Stokes equations is solved. The zeroth-order perturbation coinciding with the boundary-layer equations for vertical flat plates governs the problem. The higher-order perturbations become important near the leading edge and for large values of the inclination angle from the vertical. The assumption of zero interfacial velocity shows that, except for fluids having large (rho x mu) ratios, the results can be predicted using the vertical flat plate results by defining a modified Grashof parameter containing a cos phi term. When the interfacial shear is considered, the solutions indicate that for fluids having large (rho x mu) ratios, the heat transfer rates will be larger (approximately 15% maximum) than those predicted by the simplified model using zero interfacial velocity. In general, the inclination decreases the rate of heat transfer as well as the rate of evaporation.

Nagendra, H. R.↗
NASA NTRS1982

Analyses of Shuttle Orbiter approach and landing

A study of the Shuttle Orbiter approach and landing conditions is summarized. The causes of observed PIO-like flight deficiencies are listed, and possible corrective measures are examined. Closed-loop pilot/vehicle analyses are described, and a description is given of path-attitude stability boundaries. The latter novel approach is found to be of great value in delineating and illustrating the basic causes of this multiloop pilot control problem. It is shown that the analytical results are consistent with flight test and fixed-base simulation. Conclusions are drawn concerning possible improvements in the Shuttle Orbiter/Digital Flight Control System.

Ashkenas, I. L.↗
NASA NTRS1982

Chemorheology of reactive systems: Finite element analysis

The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.

Douglas, C.↗
NASA NTRS1983

Boundary conditions at grain boundaries

Grain boundaries in polycrystalline semiconductor material are frequently idealized as surfaces possessing a characteristic surface recombination velocity. Minority carrier densities generated by external sources (electron beams, light, etc.) in polycrystalline p-n junctions must satisfy certain boundary conditions at these grain boundaries which will be derived. It will also be shown that a 'folding technique' introduced recently to deal with this problem is of limited value.

Von Roos, O.↗
NASA NTRS1986

Turbulent relaxation processes in magnetohydrodynamics

Competing processes previously called 'selective decay' and 'dynamic alignment' are studied numerically for two-dimensional magnetohydrodynamic turbulence. In selective decay, the energy decays relatively to mean-square vector potential, and in dynamic alignment, the energy decays relatively to cross helicity. In the former case, the kinetic (fluid) energy decays to zero and the magnetic energy occupies the largest scales allowed by the boundary conditions. In the latter case, the velocity field and magnetic field become aligned and energetically equipartitioned. An extensive study of the initial value problem, with viscous and resistive dissipation, indicates that four distinct regimes of behavior are possible: a magnetically dominated regime, a velocity dominated regime, a dynamic alignment dominated regime, and a transition regime separating the others in parameter space. An analytical variational problem predicts several features seen in the computations, including geometrical alignment of velocity and magnetic fields, constraints on global quantities in the long-time limit, and in some cases, condensation to long wavelength modes.

Ting, Antonio C.↗
NASA NTRS1986

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Gottlieb, D.↗
NASA NTRS1976

A new method for solving problems of sound radiation from a duct for the case of low Mach number

A method for rapidly solving duct end-plane impedance problems is presented which is based on deriving a form of the Helmholtz integral formula expressing the normal derivative of the acoustic pressure at a boundary point. A set of integral expressions is obtained by satisfying the existing boundary conditions and then solved using a general collocation method. The results obtained for the Levine-Schwinger (1948) problem agree well with the exact values. In the case of a duct flow having a temperature mismatch with the surroundings, the results show an increase in the magnitude of the reflection coefficient for the case of a cold core, and a decrease in its value for the case of a hot core, as compared with the case of exhaust into a uniform medium. A phase change of between pi/2 and pi is nearly always achieved, which indicates the tendency towards maintaining a constant pressure at the exit plane. The method can easily be extended to arbitrary duct shapes as long as they are axisymmetric.

Wahbah, M. M.↗
NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method was developed that could predict the pressure distribution of a ducted source from far field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) was solved using explicit marching techniques. The Von Neumann method was used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach was successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗
NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method is developed that could predict the pressure distribution of a ducted source from far-field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) is solved using explicit marching techniques. The Von Neumann method is used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach is successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗
NASA NTRS1991

Generating Three-Dimensional Grids About Anything

Three-Dimensional Grids About Anything by Poisson's Equation (3DGRAPE) computer program designed to make computational grids in or about almost any shape. Generated by solution of Poisson's differential equations in three dimensions. Program automatically finds its own values for inhomogeneous terms giving near-orthogonality and controlled grid-cell height at boundaries. Grids generated applied to both viscous and inviscid aerodynamic problems, and to problems in other areas of fluid dynamics. Written in 100 percent FORTRAN 77.

Sorenson, Reese L.↗
DOE OSTI2015

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

A study of three dimensional turbulent boundary layer separation and vortex flow control using the reduced Navier Stokes equations

A reduced Navier Stokes (RNS) initial value space marching solution technique was applied to vortex generator and separated flow problems and demonstrated good predictions of the engine face flow field. This RNS solution technique using FLARE approximations can adequately describe the topological and topographical structure flow separation associated with vortex liftoff, and this conclusion led to the concept of a subclass of separations which can be called vorticity separations: separations dominated by the transport of vorticity. Adequate near wall resolution of vorticity separations appears necessary for good predictions of these flows.

Anderson, Bernhard H.↗
NASA NTRS1998

Theory of the Shape of the Heliospheric Termination Shock: Axial Symmetry

The heliospheric termination shock must exhibit asymmetry in its shape, due in part to internal latitude variations in the solar wind, and in part to the special directions defined by the external interstellar flow and/or the galactic magnetic field. This asymmetry shows up naturally in numerical simulations of the interaction between the heliosphere and local interstellar medium. However, to date only one analytical treatment of the theory has appeared, which discussed the modification of the shock shape due to solar wind latitude variations in the presence of spherically symmetric outer boundary conditions. In the present report, we discuss an extension and generalization of this theory to an axially symmetric gasdynamic system, in which departure from spherical symmetry may be due either to internal solar wind variations or to the directional properties of the external interstellar medium. It is shown that for steady flow the post-shock region is characterized by an infinite set of quantities that are conserved along streamlines; among these invariants are the stagnation pressure and a quantity closely related to vorticity. Moreover, for a given latitude profile of the (supersonic) solar wind, the geometry of the termination shock uniquely determines the valued of these invariants at the points where the streamlines emerge from the shock. A self-consistent solution of the problem thus requires a match between the shock geometry and distant boundary conditions. The theory is applied to give estimates of termination-shock asymmetry for various internal and external conditions.

Barnes, Aaron↗
DOE OSTI2016

Study of a mixed dispersal population dynamics model

In this study, we consider a mixed dispersal model with periodic and Dirichlet boundary conditions and its corresponding linear eigenvalue problem. This model describes the time evolution of a population which disperses both locally and non-locally. We investigate how long time dynamics depend on the parameter values. Furthermore, we study the minimization of the principal eigenvalue under the constraints that the resource function is bounded from above and below, and with a fixed total integral. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for the species to die out more slowly or survive more easily. Our numerical simulations indicate that the optimal favorable region tends to be a simply-connected domain. Numerous results are shown to demonstrate various scenarios of optimal favorable regions for periodic and Dirichlet boundary conditions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

A method for determining acoustic-liner admittance in ducts with sheared flow in two-cross-sectional directions

A method is developed for determining the acoustic admittance of a test liner installed in the wall of a grazing flow impedance tube. The mean flow is permitted flow gradients in both cross-sectional directions of the tube. The unknown admittance value is obtained by solving an eigenvalue problem. This eigenvalue problem results from the application of the finite-element method to the partial differential equation and boundary conditions governing the acoustic field. The credibility of the method is established by comparing results with exact solutions obtained for a constant mean-flow profile and with previous results for cases involving shear in only one cross-sectional direction. Excellent comparisons are obtained in both cases. The analysis is used in conjunction with a limited amount of experimental data and shows that the flow must be accurately modeled in order to determine the acoustic-liner properties.

Watson, W. R.↗
NASA NTRS1987

How good is the impedance boundary condition?

The impedance boundary condition (IBC) is often used in scattering problems involving material-coated conducting bodies. It is shown that for some commonly encountered coating configurations, the value of the impedance varies significantly as functions of the incident angle and polarization. Hence, the use of IBC in a rigorously formulated problem may affect the accuracy of the final solution.

Lee, Shung-Wu↗