Allan P. Rosenberg

A pseudospectral matrix element method for solution of three-dimensional incompressible flows and its parallel implementation

Abstract A new pseudospectral matrix element (PSME) method employing the primitive variable formulation of the Navier-Stokes equations was used to simulate 3-dimensional time-dependent driven cavity flow at a Reynolds number of 3200 with an aspect ratio of 3 in the spanwise direction as well as 3-dimensional flow over a backward step. The new method only requires functions which are c 0 continuous across the interface between two adjacent elements. It also ensures that the continuity equation is satisfied everywhere, in the interior (including the inter-element points) and on the boundary. The resulting complex geometry for flow over a backward step can be divided into a number of overlapping subdomains by a domain decomposition, of simpler geometry with patched grid points, in which the solution is more easily obtained. With an iterative procedure between subdomains, the complete solution is found by the Schwarz alternating procedure (SAP). With an eigenfunction expansion for the pressure, storage requirements for the 3D inversion step, O ( N 6 ), are reduced to O ( N 3 ) if the inverse of pressure equation is not stored. The parallel implementation of the three most time-consuming procedures: (i) computing the partial derivatives of scalar fields in terms of dotproduct; (ii) transforming between eigenfunction space and physical space for the pressure in terms of matrix multiplications; and (iii) performing the forward and backward sweeps of an LU decomposition to solve for the pressure have been efficiently performed on a parallel computer. The numerical results have reproduced dynamic longitudinal Taylor-Gortler-like (TGL) vortices in qualitative agreement with the experimental results of Koseff et al. and also indicated other 3-dimensional effects on the flow development. Computational results for both 2-and 3-dimensional flow over a backward-facing step at different Reynolds numbers are also presented in this paper. No pronounced 3-dimensional effects are observed for Reynolds numbers up to 450 except in the boundary layer along the spanwise direction.

A new rough surface parabolic equation program for computing low-frequency acoustic forward scattering from the ocean surface

The parabolic equation acoustic propagation program RAM has been extended to handle a rough air–water interface treated as a series of stair steps. Because much finer vertical spacing may be needed to resolve the interface than to propagate a low-frequency acoustic wave accurately in the rest of the domain, an option to use one vertical spacing near the surface and a coarser one in the rest of the ocean has been implemented. The necessary Galerkin approximations of derivatives on an unequally spaced grid have been worked out using computer algebra. The new program, Rrsfc, is efficient enough to compute the frequency spectrum of the field scattered off a moving surface by treating the surface as a sequence of frozen surfaces. A comparison of one such spectrum with actual ocean data is provided. In order to make a more detailed assessment of the program, both the depth-dependent pressure for individual surfaces and the frequency spectrum for sequences of surfaces are compared with the results of numerically exact integral equation calculations for a few constant sound speed test cases.

High frequency rough surface parabolic equation modeling for underwater acoustic communications

In this paper, we propose to develop an effective and efficient computational modeling technique to characterize the statistical properties that govern the performance and capacity of an underwater acoustic communication link. Specifically, we consider the challenging shallow water environment with a moving rough sea surface as the primary source of temporal variations. We incorporate a realistic sea surface for wind driven waves generated by the surface spectrum. We use meteorological and oceanic data measured by National Data Buoy Center (NDBC) buoy 44014 (36.611N 74.836W) and model estimates of downward radiation fluxes at its location to produce a time series, covering all of 2004 with 3 hr spacing, of the input parameters needed by the analytical spectral model. For one particular set of parameters, typical of March, we generate sea surface realizations and study their effect on acoustic propagation. We extend a parabolic equation (PE) model to compute the propagation of a high frequency, wide-band acoustic transmission with a time-varying sea surface. We provide numerical results of received signal power as a function of range and depth. Our modeling approach has both physical applicability and computation feasibility to generate channel impulse responses useful for adaptive underwater communications.

Coherent and differential acoustic communication in shallow water using transmitter and receiver arrays

Underwater acoustic communication link performance is investigated under strong time-frequency variation. A state of the art split-step parabolic equation program was used to generate channel responses under a moving rough sea surface. A shallow water environment with 47.5m depth at 1km range was considered, with the sea surface characterized as a mature sea under a 10m/s (at 10m height) wind. OFDM signal structure with a reasonable trade-off between symbol duration and subcarrier bin width is found to address only partially the severely overspread channel. It is found that beamforming at the transmitter and at the receiver significantly improves both coherence time and frequency, allowing doubling of the effective throughput. Further improvement of the rate is achieved through differential modulation which avoids training overhead. A link with 4 transmitters and 10 receivers was found to support 1.8 bps/Hz effective rate at 1km using differential modulation on each OFDM subcarrier, more than 4 times the corresponding rate of a 1×1 link using pilot-based estimation and non-differential modulation on each OFDM subcarrier.

An accurate, efficient rough surface parabolic equation program

The parabolic equation program Fepe has been extended to handle a rough air–water interface treated as a series of stair steps. Because much finer vertical spacing may be needed to resolve the interface than to propagate an acoustic wave accurately in the rest of the domain, an option to use one vertical spacing near the surface and a coarser one in the rest of the ocean has been implemented. The necessary Galerkin approximations of derivatives on an unequally spaced grid have been worked out using the symbolic manipulation program Mathematica. A test case with a realistic surface is provided to demonstrate the accuracy of the new program Fepe–rsfc. The code is efficient enough to allow thousands of runs for realistic sized problems, for example to simulate the effect of a moving surface. [Work supported by the office of the Chief of Naval Operations.]

Forward-looking engineering concepts for ultrasonic modulation of neural circuit activity in humans

We examine the potential for low-intensity focused ultrasound to non-invasively produce small (< 1mm3) focal acoustic fields for precise brain stimulation near the skull. Our goal is to utilize transcranial ultrasonic neuromodulation to transform communications and immersive gaming experiences and to optimize neuromodulation applications in medicine. To begin evaluating possible hardware design strategies for engineering ultrasonic brain interfaces, in the present study we evaluated the skull transmission properties of longitudinal and shear waves as a function of incidence angle for 0–2 MHz. We also employed K-wave and time-reversal numerical simulations to further inspect waveform interactions with modeled layers. Timereversal focusing for single-layer and three-layer skull cases were simulated for three different bandwidth ranges (MHz): Broadband(0–2), 1 MHz(0.4–1.4), and 0.2 MHz(0.4–0.6). Broadband and 1 MHz bandwidths emulate the performance of micromachined or piezo membrane ultrasonic arrays, while 0.2 MHz bandwidth is representative of the performance of conventional piezoelectric ultrasonic transducer. We found the 3dB focal volume was ~0.6 mm for broadband and 1 MHz, with the latter showing a slightly larger sidelobe. In contrast, 0.2 MHz nearly doubled the size of the 3dB focal volume while producing prominent sidelobes. Our results provide initial confirmation that a broadband, ultrasonic, linear array can access the first 15 mm of the human brain, which contains circuitry essential to sensory processing including pre-motor and motor planning, somatosensory feedback, and visual attention. These areas are critical targets for providing haptic feedback via non-invasive neural stimulation.

Acoustical experimental design for ultrasonic neurostimulation on rodents

While the mechanisms of ultrasonic neurostimulation are still unknown, this method has been successfully shown on rodents from a variety of research groups. While the results are compelling, there has been limited work in characterizing the acoustic fields that are generated and ultimately delivered to the rodent brain which is important in order to determine the underlying neurostimulation mechanism. This presentation details some of the acoustical experimental design processes that are being undertaken at JHU/APL as well as our current progress in the rodent ultrasonic neurostimulation. The experimental design utilizes a complementary process of both simulation and experimentation verification to determine the expected delivered acoustic wave field. The simulation encompasses the full propagation path from the single element focused transducer, through an acoustic waveguide and skull, to the treatment location. This work uses a focused transducer with a center frequency of 0.5 MHz with several different waveguides that are characterized in our calibration tank with regards to intensity over space. Each of these waveguides is modeled and compared relative to the focal spot size and intensity delivered to the focal spot. These measurements are used to select an optimal waveguide which is used in the model to determine the expected performance of the full system. The presented results compare the performance of the waveguides and their impact on ultrasonic delivery to the rodent brain.While the mechanisms of ultrasonic neurostimulation are still unknown, this method has been successfully shown on rodents from a variety of research groups. While the results are compelling, there has been limited work in characterizing the acoustic fields that are generated and ultimately delivered to the rodent brain which is important in order to determine the underlying neurostimulation mechanism. This presentation details some of the acoustical experimental design processes that are being undertaken at JHU/APL as well as our current progress in the rodent ultrasonic neurostimulation. The experimental design utilizes a complementary process of both simulation and experimentation verification to determine the expected delivered acoustic wave field. The simulation encompasses the full propagation path from the single element focused transducer, through an acoustic waveguide and skull, to the treatment location. This work uses a focused transducer with a center frequency of 0.5 MHz with several different...

Sensitivity analysis of acoustic channel characteristics to sea surface spectral uncertainty.

The interaction of sound with the sea surface is important for underwater acoustic communications. The high‐frequency sound used, 10 kHz and above, is sensitive to surface wave frequencies well above the ∼0.5‐Hz upper limit routinely measured by wave buoys. Accurately measuring the surface in the short gravity wave regime is difficult and even the general shape of the spectrum is uncertain. The primary measurement challenge is to disentangle the effects of the instrument, including its supporting structure, from what one is attempting to measure. There have been attempts to combine the copious data at low frequencies and the sparse data at higher frequencies to produce model spectra depending on a few parameters that describe the spectrum in the short gravity wave region and above. In this work we study the sensitivity of the acoustic channel characteristics such as the channel impulse response to our uncertain spectral knowledge. We merge low‐frequency surface wave spectra measured at NDBC 44014, with va...

Approaches to accelerate three‐dimensional acoustic propagation models

A three‐dimensional split‐step Pade parabolic‐equation approach [J. Comput. Acoust. 9(2), 17–39 (2001)] was developed as an extension to Collins and Chin‐Bings algorithm [J. Acoust. Soc. Am. 87, 1104–1109 (1990)] to account for azimuthal acoustic refraction via a narrow‐angle approximation. It was shown that high accuracy requires fine azimuthal and range step sizes. Therefore, a couple of Pade terms are sufficient given the required small range step size. The paper also mentions the possible implementation of a variable azimuthal grid size, where the number of azimuthal segments increases proportionally with increasing range, as another approach to boost the models computational speed. In this talk, we investigate the possibility of azimuthal padding as another approach to speed‐up the model when the user is only interested in propagating the acoustic field along a wedge of azimuthal angles instead of the entire 360.