Results for “high-frequency wave equations” — Page 3

NASA NTRS1997

Using High-Order Methods on Lower-Order Geometries

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.

Casper, Jay↗

NASA NTRS2007

Radar Interferometer for Topographic Mapping of Glaciers and Ice Sheets

A report discusses Ka-band (35-GHz) radar for mapping the surface topography of glaciers and ice sheets at high spatial resolution and high vertical accuracy, independent of cloud cover, with a swath-width of 70 km. The system is a single- pass, single-platform interferometric synthetic aperture radar (InSAR) with an 8-mm wavelength, which minimizes snow penetration while remaining relatively impervious to atmospheric attenuation. As exhibited by the lower frequency SRTM (Shuttle Radar Topography Mission) AirSAR and GeoSAR systems, an InSAR measures topography using two antennas separated by a baseline in the cross-track direction, to view the same region on the ground. The interferometric combination of data received allows the system to resolve the pathlength difference from the illuminated area to the antennas to a fraction of a wavelength. From the interferometric phase, the height of the target area can be estimated. This means an InSAR system is capable of providing not only the position of each image point in along-track and slant range as with a traditional SAR but also the height of that point through interferometry. Although the evolution of InSAR to a millimeter-wave center frequency maximizes the interferometric accuracy from a given baseline length, the high frequency also creates a fundamental problem of swath coverage versus signal-to-noise ratio. While the length of SAR antennas is typically fixed by mass and stowage or deployment constraints, the width is constrained by the desired illuminated swath width. As the across-track beam width which sets the swath size is proportional to the wavelength, a fixed swath size equates to a smaller antenna as the frequency is increased. This loss of antenna size reduces the two-way antenna gain to the second power, drastically reducing the signal-to-noise ratio of the SAR system. This fundamental constraint of high-frequency SAR systems is addressed by applying digital beam-forming (DBF) techniques to synthesize multiple simultaneous receive beams in elevation while maintaining a broad transmit illumination. Through this technique, a high antenna gain on receive is preserved, thereby reducing the required transmit power and thus enabling high-frequency SARs and high-precision InSAR from a single spacecraft.

Moller, Delwyn K.↗