Perturbation of solutions of differential equations satisfying general boundary conditions
Perturbation of solutions of system of nonlinear differential equations under general linear boundary conditions
Lewis, D. C.↗
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Nonlinear theory of inviscid Taylor instability near the cutoff wavenumber.
Taylor instability nonlinear oscillations, obtaining uniform solutions for wavenumbers near and larger than cut-off
Kiang, R. L.↗
Some applications of NASTRAN to the buckling of thin cylindrical shells with cutouts
The buckling of isotropic and waffle-stiffened circular cylinders with and without cutouts was studied using NASTRAN's Rigid Format 5 for the case of axial compressive loading. The results obtained for the cylinders without cutouts are compared with available reference solutions. The results for the isotropic cylinders containing a single circular cutout with selected radii are compared with available experimental data. For the waffle-stiffened cyclinder, the effect of two diametrically opposed rectangular cutouts was studied. A DMAP alter sequence was used to permit the necessary application of different prebuckling and buckling boundary conditions. Advantage was taken of available symmetry planes to formulate equivalent NASTRAN model segments which reduced the associated computational cost of performing the analyses. Limitations of the applicability of NASTRAN for the solution of problems with nonlinear characteristics are discussed.
Williams, J. G.↗
Backlund transformation for solutions of the Korteweg-de Vries equation
We present a Backlund transformation operating on solutions of the Korteweg-de Vries equation. It provides a unifying approach to the theory of solitary waves (solutions). Recursive application of the transformation to any solution of the Korteweg-de Vries equation generates a hierarchy of solutions for which an algebraic recursion relation is obtained. Every such hierarchy (one of which is the known family of pure multisoliton solutions) thus admits a nonlinear superposition principle.
Wahlquist, H. D.↗
Time scales for molecule formation by ion-molecule reactions
Analytical solutions are obtained for nonlinear differential equations governing the time-dependence of molecular abundances in interstellar clouds. Three gas-phase reaction schemes are considered separately for the regions where each dominates. The particular case of CO, and closely related members of the Oh and CH families of molecules, is studied for given values of temperature, density, and the radiation field. Nonlinear effects and couplings with particular ions are found to be important. The time scales for CO formation range from 100,000 to a few million years, depending on the chemistry and regime. The time required for essentially complete conversion of C(+) to CO in the region where the H3(+) chemistry dominates is several million years. Because this time is longer than or comparable to dynamical time scales for dense interstellar clouds, steady-state abundances may not be observed in such clouds.
Langer, W. D.↗
A method for developing K/S boundary conditions
A method for developing the missing general K/S (Kustaanheimo/Stiefel) boundary conditions is presented, with use of the formalism of optimal control theory. As illustrative examples, the method is applied to the transfer between two position and velocity vectors and to the K/S Lambert problem to derive the missing terminal conditions. The necessary equations for a solution are then developed to the K/S Lambert problem with both the fictitious time, s, and the generalized eccentric anomaly, E, as the independent variables. The latter formulation, requiring the solution of only one nonlinear, well-behaved equation in one unknown, E, results in considerable simplification of the problem. This simplification is possible because the energy equation, in the E-formulation, is separable.
Jezewski, D. J.↗
K/S two-point-boundary-value problems
A method for developing the missing general K/S (Kustaanheimo/Stiefel) boundary conditions is presented, with use of the formalism of optimal control theory. As an illustrative example, the method is applied to the K/S Lambert problem to derive the missing terminal condition. The necessary equations are developed for a solution to this problem with the generalized eccentric anomaly, E, as the independent variable. This formulation, requiring the solution of only one nonlinear, well-behaved equation in one unknown, E, results in considerable simplification of the problem.
Jezewski, D. J.↗
An efficient procedure for computing partial ionization of a gas in numerical fluid dynamics
A numerical procedure is described that allows efficient solution for the three nonlinear and implicit equations of state relating the equilibrium properties of a partially (and singly) ionized neutral gas. In the computation, the values for the intensive variables, that is pressure, temperature and ionization coefficient, are iteratively obtained with a given accuracy starting from assigned values for energy and volume per unit mass. Iterative computation is performed only when the value for the ionization coefficient lies within the lower and the upper bounds fixed by the required number of significant digits; otherwise the two explicit equations of state for nonionized or for fully ionized gases are employed.
Garribba, S.↗
NEWSUMT: A FORTRAN program for inequality constrained function minimization, users guide
A computer program written in FORTRAN subroutine form for the solution of linear and nonlinear constrained and unconstrained function minimization problems is presented. The algorithm is the sequence of unconstrained minimizations using the Newton's method for unconstrained function minimizations. The use of NEWSUMT and the definition of all parameters are described.
Miura, H.↗
A split finite element algorithm for the compressible Navier-Stokes equations
An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.
Baker, A. J.↗
Radiation damping of long, finite-amplitude internal waves
Numerical solutions of a damped, nonlinear wave equation are presented. The equation describes the propagation of waves in a narrow thermocline or inversion which lose energy by exciting internal waves in the weakly stratified ambient environment. The results provide estimates for the persistence of finite-amplitude internal waves propagating in a thermoclinic waveguide.
Pereira, N. R.↗
Possible fluid dynamical interpretation of some reported features in the Jovian atmosphere
A fluid dynamical interpretation is presented of the two major types of disturbance found in the southern hemisphere of Jupiter by the Voyager 1 imaging data. The observed features always occur together, and consist of a compact elliptically shaped formation having an anticyclonic flow which is poleward of a pair of more elongated cyclonic structures, as in the Great Red Spot and the white ovals. It is noted that the anticyclonic features at 41 deg S may be described by the cnoidal wave solutions to the appropriate nonlinear evolution equation, and that flow patterns derived in the vicinity of the Great Red Spot and white ovals are strikingly similar to those obtained for the flow around a solitary wave of the type than can exist in a zonal flow such as that found in the Jupiter atmosphere. Results of computations in terms of solitary wave theory of flow fields in the atmospheric structure and zonal velocity profiles determined from Voyager infrared spectroscopy and radiometry data are then presented which show that the pattern must be a singular solitary wave mode, the east-west structure of which is best described by the Korteweg-de-Vries equation
Maxworthy, T.↗
Optimality criteria solution strategies in multiple constraint design optimization
Procedures and solution strategies are described to solve the conventional structural optimization problem using the Lagrange multiplier technique. The multipliers, obtained through solution of an auxiliary nonlinear optimization problem, lead to optimality criteria to determine the design variables. It is shown that this procedure is essentially equivalent to an alternative formulation using a dual method Lagrangian function objective. Although mathematical formulations are straight-forward, successful applications and computational efficiency depend upon execution procedure strategies. Strategies examined, with application examples, include selection of active constraints, move limits, line search procedures, and side constraint boundaries.
Levy, R.↗
Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code
Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.
Manro, M. E.↗
Multiple buoyancy driven flows in a vertical cylinder heated from below
The structure of axisymmetric buoyancy-driven convection in a vertical cylinder heated from below is probed by finite element solution of the Boussinesq equations coupled with computed-implemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with Prandtl number of one and for cylinders with aspect ratio (Lambda) (defined as the height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curve for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous evolution of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shear-free sidewalls. The smooth transitions in flow structure with Rayleigh number and lambda are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Lambda or = Lambda * approximately 0.80 or by a limit point for Lambda Lambda *. The transition between these two modes may be described by the theory of multiple limit point bifurcation.
Yamaguchi, Y.↗
The CMC/3DPNS computer program for prediction of three-dimension, subsonic, turbulent aerodynamic juncture region flow. Volume 2: Users' manual
The CMC fluid mechanics program system was developed to transmit the theoretical solution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. Data procedures for the CMC 3 dimensional Parabolic Navier-Stokes (PNS) algorithm are presented. General data procedures a juncture corner flow standard test case data deck is described. A listing of the data deck and an explanation of grid generation methodology are presented. Tabulations of all commands and variables available to the user are described. These are in alphabetical order with cross reference numbers which refer to storage addresses.
Manhardt, P. D.↗
High temperature thermomechanical analysis of ceramic coatings
This paper investigates the thermomechanical response of ceramically coated metal parts in elevated thermal environments. This is made possible through the development of an improved finite element algorithm that enables the efficient and stable solution of the inherently nonlinear elastic-creep (inelastic) type thermomechanical field equations associated with high temperature. Based on the improved algorithm, the results of several numerical experiments are presented. These illustrate the significant influence of inelastic behavior in generating residual stress fields.
Padovan, J.↗
The CMC/3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 3: Programmers' manual
The CMC fluid mechanics program system was developed to transmit the theoretical evolution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. A detailed view of the code from the standpoint of a computer programmer's use is presented. A system macroflow chart and detailed flow charts of several routines necessary to interact with a theoretican/user to modify the operation of this program are presented. All subroutines and details of usage, primarily for input and output routines are described. Integer and real scalars and a cross reference list denoting subroutine usage for these scalars are outlined. Entry points in dynamic storage vector IZ; the lengths of each vector accompanying the scalar definitions are described. A listing of the routines peculiar to the standard test case and a listing of the input deck and printout for this case are included.
Orzechowski, J. A.↗