Solving the shallow water equations on the Cray X-MP/48 and the connection machine 2

The shallow water equations in Cartesian coordinates and 2-D are solved on the Connection Machine 2 (CM-2) using both the spectral and finite difference methods. A description of these implementations is presented together with a brief discussion of the CM-2 as it relates to these specific computations. The finite difference code was written both in C* and *LISP and the spectral code was written in *LISP. The performance of the codes is compared with a FORTRAN version that was optimized for the Cray X-MP/48

Revisiting Event Horizon Finders

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time to be most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10^5. Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only {\em some} of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.Comment: 30 pages, 15 figures, revision

Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure

A computational study of the effect of windscreen shape and flow resistivity on turbulent wind noise reduction

This is the published version. Copyright 2011 Acoustical Society of AmericaIn this paper, numerical simulations are used to study the turbulentwind noise reduction effect of microphone windscreens with varying shapes and flow resistivities. Typical windscreen shapes consisting of circular, elliptical, and rectangular cylinders are investigated. A turbulent environment is generated by placing a solid circular cylinder upstream of the microphone. An immersed-boundary method with a fifth-order weighted essentially non-oscillatory scheme is implemented to enhance the simulation accuracy for high-Reynolds number flow around the solid cylinder as well as at the interface between the open air and the porous material comprising the windscreen. The Navier–Stokes equations for incompressible flow are solved in the open air. For the flow inside the porous material, a modified form of the Zwikker–Kosten equation is solved. The results show that, on average, the circular and horizontal ellipse windscreens have similar overall wind noise reduction performance, while the horizontal ellipse windscreen with medium flow resistivity provides the most effective wind noise reduction among all the considered cases. The vertical ellipse windscreen with high flow resistivity, in particular, increases the wind noise because of increased self-generation of turbulence

Dynamics of the speed changes control device with differential gear and closed-loop hydraulic system through the sun gear

Розглянуті та досліджені динамічні процеси у пристрої для керування змінамишвидкості з зубчастою диференціальноюпередачеюі замкнутою гідросистемою через сонячне зубчасте колесо, коли ведучою ланкою є водило, а веденою – епіцикл. Розроблена математична модель та розв’язані рівняння динаміки таких пристроїв залежно від умов їх роботи. Отримані результати є підґрунтям для подальшого комп’ютерного моделювання та проведення кількісного аналізу з метоюоцінки роботи гідромеханічного приводу та вибору необхідної замкнутої гідросистеми для керування змінамишвидкості.Dynamic processes in speed changes control device with differential gear transmission and closed loop hydraulic system have been considered and investigated for the case when the sun gear is a control link, carrier is a driving link and the ring gear is driven. The motion of the system has been modeled in a formalized form using the Lagrange’s equation of the second kind. For this purpose, the expression for the energy of such speed changes control device has been derived. Then, based on the Lagrange’s equation of second kind, a system of differential equations for the motion of the links has been obtained and solved. The solution of the system of equations of dynamics of such devices is the basis for further computer simulation and quantitative analysis in order to evaluate the operation of such devices and to select the necessary closed loop hydraulic system to control changes in speed, when the load changes periodically over a long time; or when the magnitude of the shock load after a sharp increase remains unchanged for either a long time or a small time; or the actuator stops immediately because of a significant overload