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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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Resonant oscillations of intermediate frequency in a stratified atmosphere.

A class of solutions to a model of forced oscillations in a rotating stratified atmospheric layer is derived and analyzed. The basic model is found to reduce to a boundary value problem with a second-order linear partial differential equation of the hyperbolic type for this range of forcing frequencies. The forced solutions are shown to exhibit resonances with the normal modes of oscillation of the layer. The characteristics of the resonant modes are analyzed in terms of mean tropospheric values of temperature, temperature lapse, wind speed, horizontal and vertical wind shears, latitude, and the frequency and horizontal wavelength of the forcing mechanism. These solutions are compared with solutions to the model for a different (subinertial) range of forcing frequencies. This comparison leads to an elliptic boundary value problem. The solutions in that case do not exhibit the same type of resonance and generally decay away from the region of forcing.

Thompson, O. E.↗
NASA NTRS1984

Stability of the laminar boundary layer in a streamwise corner

The stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary layer problem is examined. The semi-infinite boundary value problem satisfied by small amplitude disturbances in the "bending boundary layer' region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid "first approximations' to solutions of the governing differential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an approximate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two dimensional boundary layer profiles.

Lakin, W. D.↗
NASA NTRS1984

Stability of the laminar boundary layer in a streamwise corner

The stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary layer problem is examined. The semi-infinite boundary value problem satisfied by small amplitude disturbances in the 'bending boundary layer' region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid 'first approximations' to solutions of the governing differential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an approximate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two dimensional boundary layer profiles. Previously announced in STAR as N84-17532

Lakin, W. D.↗
NASA NTRS1984

Navier-Stokes calculations for unsteady three-dimensional vortical flows in unbounded domains

Finite-difference Navier-Stokes calculations for unsteady, three-dimensional, incompressible, viscous flows induced by initial vorticity distributions are presented and discussed in this paper. The initial vorticity distributions are assumed to be embedded in a flow field of infinite extent that is quiescent at infinity. These vorticity distributions are typical of vortex rings and other closed vortical tubes or structures. Such structures are important elements in fluid flows such as jets, atmospheric convection and the far-field wakes of aircraft; studies of their interaction may aid in an understanding of complex fluid flows. The calculations employ a method recently proposed by Ting to approximate the infinite-domain boundary value problem with a finite boundary computational domain, and this method is shown to yield accurate three-dimensional results for reasonable expenditures of computer time. Because of the efficiency of the boundary condition technique and the resulting Navier-Stokes code, a 16-bit minicomputer with virtual memory was capable of performing the calculations for the unsteady motion of two obliquely colliding vortex rings. The results of these calculations are presented in the paper.

Chamberlain, J. P.↗
NASA NTRS1995

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

Oden, J. Tinsley↗
NASA NTRS1995

Adaptive Finite Element Methods for Continuum Damage Modeling

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

Min, J. B.↗
NASA NTRS1988

An exact inverse method for subsonic flows

A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.

Daripa, Prabir↗
NASA NTRS1976

Quasi-three-dimensional laminar boundary-layer separations in supersonic flow

A numerical algorithm is presented for solving laminar, steady, supersonic interacting boundary-layer flows for quasi-three-dimensional configurations. The interaction problem is treated as a boundary-value problem and a salient feature of the scheme is the direct implementation of the downstream boundary condition. Solutions are presented for axisymmetric and swept (yawed) compression ramps for both adiabatic and heat transfer conditions over a Mach number range of 2-6. The results are in good agreement with experimental data and existing theories for axisymmetric cases. For the swept (yawed) configurations, lack of experimental data makes a direct comparison impossible, but the present solutions are found to be in qualitative agreement with earlier studies. In addition it is shown that the trends obtained here for the sweep effects are well predicted by a simple extension of the two-dimensional asymptotic theory.

Vatsa, V. N.↗
NASA NTRS1987

A fast approach to designing airfoils from given pressure distribution in compressible flows

A new inverse method for aerodynamic design of airfols is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arc length of the as-yet unknown body. This inverse problem is shown to be mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the freestream Mach number, and the upstream flow direction. The existence of a solution to a given pressure distribution is discussed. The method is easy to implement and extremely efficient. A series of results for which comparisons are made with the known airfoils is presented.

Daripa, Prabir↗
NASA NTRS1987

An efficient method for inverse problems

A new inverse method for aerodynamic design of subcritical airfoils is presented. The pressure distribution in this method can be prescribed in a natural way, i.e. as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving a single nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the free stream Mach number M(sub x) and the upstream flow direction theta(sub x). The existence of a solution for any given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils.

Daripa, Prabir↗