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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Perfectly Matched Layer for Linearized Euler Equations in Open and Ducted Domains

Recently, perfectly matched layer (PML) as an absorbing boundary condition has widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave mode are dispersive. It will be shown that the group velocity and phase velocity of these modes can have opposite signs. This results in a confined environment, PML may not be suitable as an absorbing boundary condition.

Tam, Christopher K. W.↗
NASA NTRS1992

Efficient yet accurate solution of the linear transport equation in the presence of internal sources - The exponential-linear-in-depth approximation

The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.

Kylling, Arve↗
NASA NTRS1991

Prediction of unsteady aerodynamic loads in cascades using the linearized Euler equations on deforming grids

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. Using the linearized Euler technique, one decomposes the flow into a mean (or steady) flow plus an unsteady, harmonically varying, small disturbance flow. Linear variable coefficient equations describe the small disturbance behavior of the flow, and are solved using a pseudo-time marching Lax-Wendroff scheme. For the blade motion problem, a harmonically deforming computational rid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition. The paper also presents a new, numerically exact, nonreflecting far-field boundary condition based on an eigenanalysis of the discretized equations. Computed flow solutions demonstrate the computational accuracy and efficiency of the present method. The solution of the linearized Euler equations requires one to two orders of magnitude less computer time than solution of the nonlinear Euler equations using traditional time-accurate time-marching techniques. In addition, the deformable grid significantly improves the accuracy of the solution.

Hall, Kenneth C.↗
NASA NTRS1971

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Stone, H. S.↗
NASA NTRS1973

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations.

Tridiagonal linear systems of equations can be solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computation on computers of the Illiac IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log(sub-2) N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Stone, H. S.↗
NASA NTRS1980

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗
NASA NTRS1986

Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations

Linearized alternating direction implicit (ADI) forms of a class of total variation diminishing (TVD) schemes for the Euler and Navier-Stokes equations have been developed. These schemes are based on the second-order-accurate TVD schemes for hyperbolic conservation laws developed by Harten (1983, 1984). They have the property of not generating spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1-2 grid points. These schemes are relatively simple to understand and easy to implement into a new or existing computer code. One can modify a standard three-point central-difference code by simply changing the conventional numerical dissipation term into the one designed for the TVD scheme. For steady-state applications, the only difference in computation is that the current schemes require a more elaborate dissipation term for the explicit operator; no extra computation is required for the implicit operator. Numerical experiments with the proposed algorithms on a variety of steady-state airfoil problems illustrate the versatility of the schemes.

Yee, H. C.↗
NASA NTRS1976

A quasi-linear kinetic equation for cosmic rays in the interplanetary medium

A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.

Luhmann, J. G.↗
NASA NTRS1996

On the Retrieval of Lightning Radio Sources from Time-of-Arrival Data

We examine the problem of retrieving three-dimensional lightning locations from radio frequency Time-Of-Arrival (TOA) measurements. Arbitrary antenna locations are considered. By judiciously differencing measurements that are related to the location of the antennas and their excitation times, the problem is converted from the initial spherical nonlinear form to a system of linear equations. In the linear formalism, the source location and time-of-occurrence is viewed geometrically as an intersection of hyperplanes in the four-dimensional Minkowski space (x,y,z,t). The linear equations are solved to obtain explicit analytic expressions for the location and time variables. Retrieval errors are not interpreted with conventional Geometrical Dilution of Precision (GDOP) arguments as discussed by Holmes and Reedy (1951), but with more recent inversion analyses considered by Twomey (1977). Measurement errors are propagated analytically so that the specific effect of these errors on the solution is clarified. The sensitivity of the solution on the number of antennas used, antenna network geometry, source position, and measurement differencing schemes are discussed in terms of the eigenvalues of the linear system.

Koshak, William J.↗