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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Changing stepsize in the integration of differential equations using modified divided differences

Multistep methods for solving differential equations based on numerical integration formulas or numerical differentiation formulas (for stiff equations) require special provision for changing the stepsize. New algorithms are given which make the use of modified divided differences an attractive way to carry out the change in stepsize for such methods. Error estimation and some of the important factors in stepsize selection and the selection of integration order are also considered.

Krogh, F. T.↗
NASA NTRS1963

Application of Dorodnitsyn's Integral Method to Nonequilibrium Flows over Pointed Bodies

Dorodnitsyn's integral method is used to obtain an approximate solution to the supersonic nonequilibrium flow over pointed bodies with attached shock waves. The partial differential equations governing the flow are converted to an approximate set of ordinary equations, which are solved by numerical integration starting at the body tip. Detailed analytical and numerical results for the first approximation are presented, considering the vibrational relaxation of a diatomic gas over a wedge or cone. It is shown that the first approximation yields: (1) The exact flow-variable gradients at the wedge tip (2) Expressions for the flow-variable gradients at the cone tip which are in agreement with extrapolations of characteristics calculations (3) A good approximate algebraic solution for frozen or equilibrium conical flow (4) An approximate expression for the nonequilibrium-flow stream function which affords a means of obtaining variations across the shock layer of the temperature and vibrational energy. Numerical results for both the wedge and cone compare favorably with identical cases computed by the method of characteristics.

NONEQUILIBRIUM FLOW↗
NASA NTRS1966

A study of pulsation in RR Lyrae models.

Nonlinear calculations of intermediate amplitude to analyze stability of pulsating stars of varying composition, mass, luminosity, etc, using numerical integration of motion equations

STELLAR MASS↗
NASA NTRS1979

The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators

The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.

Bainum, P. M.↗
NASA NTRS1986

A combined integrating and differentiating matrix formulation for boundary value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗
NASA NTRS1986

A combined integrating- and differentiating-matrix formulation for boundary-value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗
NASA NTRS1988

Problems in fluid dynamics

A scheme was developed for the parametric differentiation and integration of gas dynamics equations. A numerical integration of the gas dynamics equations is necessarily performed for a specific set of parameter values. The linear variational equations are obtained by differentiating the exact equations with respect to each of the relevant parameters. The resulting matrix of flow quantities is referred to as the Jacobi matrix. The subsequent procedure is then straightforward. The method was tested for two dimensional supersonic flow past an airfoil, with airfoil thickness, camber, and angle of attack varied. This approach has great potential value for rapidly assessing the effect of design changes. The other focus of the work was on problems in fluid stability, bifurcations, and turbulence.

Sirovich, Lawrence↗
NASA NTRS1991

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility being the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements. Recent efforts have focused on reducing run time, improving accuracy and adding more boundary condition choices.

Klang, Eric C.↗
NASA NTRS1990

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility is the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements.

Owen, Vicki L.↗
NASA NTRS1995

High-speed correction factor to the O(+)-O resonance charge exchange collision frequency

The high-speed correction factor to the O(+)-O collision frequency, resulting from drift velocities between ions and neutrals, is calculated by solving the integral expression in this factor both numerically and analytically. Although the analytic solution is valid for either small or large drift velocities between ions and neutrals, for temperatures of interest and all drift velocities considered, agreement is found between analytic and detailed numerical integration results within less than 1% error. Let T(sub r) designate the average of the ion and neutral temperatures in K, and u = nu(sub d)/alpha, where nu(sub d) is the relative drift velocity in cm/s, and alpha = 4.56 x 10(exp 3) square root of T(sub r) cm/s is the thermal velocity of the O(+)-O system. Then, as u ranges from 0 to 2, the correction factor multiplying the collision frequency increases monotonically from 1 to about 1.5. An interesting result emerging from this calculation is that the correction factor for temperatures of aeronomical interest is to a good approximation independent of the temperature, depending only on the scaled velocity u.

Omidvar, K.↗
NASA NTRS1984

A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.

Radhakrishnan, K.↗