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Gabrielsen, R. E.

Publications and source records attributed to Gabrielsen, R. E..

10 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Gabrielsen, R. E.↗
NASA NTRS1981

A solution for two-dimensional Fredholm integral equations of the second kind with periodic, semiperiodic, or nonperiodic kernels

A numerical scheme for solving two dimensional Fredholm integral equations of the second kind is developed. The proof of the convergence of the numerical scheme is shown for three cases: the case of periodic kernels, the case of semiperiodic kernels, and the case of nonperiodic kernels. Applications to the incompressible, stationary Navier-Stokes problem are of primary interest.

Gabrielsen, R. E.↗
NASA NTRS1981

Reduction of the two dimensional stationary Navier-Stokes problem to a sequence of Fredholm integral equations of the second kind

Present approaches to solving the stationary Navier-Stokes equations are of limited value; however, there does exist an equivalent representation of the problem that has significant potential in solving such problems. This is due to the fact that the equivalent representation consists of a sequence of Fredholm integral equations of the second kind, and the solving of this type of problem is very well developed. For the problem in this form, there is an excellent chance to also determine explicit error estimates, since bounded, rather than unbounded, linear operators are dealt with.

Gabrielsen, R. E.↗
NASA NTRS1980

A solution of one dimensional Fredholm integral equations of the second kind

Fredholm integral equations of the second kind of the one dimension are numerically solved. It is proven that the numerical solution converges to the exact solution of the integral equation. This is shown for periodic kernels and then extended to nonperiodic kernels. This development helps delineate a basic theory which has the potential of solving very complex problems.

Gabrielsen, R. E.↗
NASA NTRS1977

Accuracy of the Kirchoff formula in determining acoustic shielding with the use of a flat plate

It has been suggested that if jet engines of aircraft were placed at above the wing instead of below it, the wing would provide a partial shielding of the noise generated by the engines relative to observers on the ground. The shielding effects of an idealized three-dimensional barrier in the presence of an idealized engine noise source was predicted by the Kirchoff formula. Based on the good agreement between experimental measurements and the numerical results of the current study, it was concluded that the Kirchoff approximation provides a good qualitative estimate of the acoustic shielding of a point source by a rectangular flat plate for measurements taken in the far field of the flat plate at frequencies ranging from 1 kHz to 20 kHz. At frequencies greater than 4 kHz the Kirchoff approximation provides accurate quantitative predictions of acoustic shielding.

Gabrielsen, R. E.↗
NASA NTRS1977

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Davis, J. E.↗
NASA NTRS1975

Algorithm for nonlinear stationary Navier-Stokes problem

Results of applications of algorithm suggest that it has potential application to variety of related fluid flow problems, such as presently intractable separation problem of aerodynamics. Details of mathematical development, as well as computation of explicit error estimates, are available.

Gabrielsen, R. E.↗