Symbolic computation and perfect fluids in general relativity

Focuses on two areas within the field of general relativity. Firstly, the history and implications of the long-standing conjecture that general relativistic, shear-free perfect fluids which obey a barotropic equation of state p = p(w) such that w + p = 0, are either non-expanding or non-rotating. Secondly the application of the computer algebra system Maple to the area of tetrad formalisms in general relativity.

The fluid mechanics of a two-dimensional Aaberg exhaust hood

In this paper a study of the air flow pattern created by a two-dimensional Aaberg exhaust hood local ventilation system is presented. A mathematical model of the flow, in terms of the stream function ψ, is derived analytically for both laminar and turbulent injections of fluid. Streamlines and lines of constant speed deduced from the model are examined for various values of the governing dimensionless operating parameter and predictions are given as to the area in front of the hood from which the air can be sampled. The effect of the injection of fluid on the centre-line velocity of the flow is examined and a comparison of the results with the available experimental data is given. © 1992.

Adapting data processing to compare model and experiment accurately: A discrete element model and magnetic resonance measurements of a 3d cylindrical fluidized bed

Discrete element modeling is being used increasingly to simulate flow in fluidized beds. These models require complex measurement techniques to provide validation for the approximations inherent in the model. This paper introduces the idea of modeling the experiment to ensure that the validation is accurate. Specifically, a 3D, cylindrical gas-fluidized bed was simulated using a discrete element model (DEM) for particle motion coupled with computational fluid dynamics (CFD) to describe the flow of gas. The results for time-averaged, axial velocity during bubbling fluidization were compared with those from magnetic resonance (MR) experiments made on the bed. The DEM-CFD data were postprocessed with various methods to produce time-averaged velocity maps for comparison with the MR results, including a method which closely matched the pulse sequence and data processing procedure used in the MR experiments. The DEM-CFD results processed with the MR-type time-averaging closely matched experimental MR results, validating the DEM-CFD model. Analysis of different averaging procedures confirmed that MR time-averages of dynamic systems correspond to particle-weighted averaging, rather than frame-weighted averaging, and also demonstrated that the use of Gaussian slices in MR imaging of dynamic systems is valid. © 2013 American Chemical Society.

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A framework for network RTK data processing based on grid computing

Real-Time Kinematic (RTK) positioning is a technique used to provide precise positioning services at centimetre accuracy level in the context of Global Navigation Satellite Systems (GNSS). While a Network-based RTK (N-RTK) system involves multiple continuously operating reference stations (CORS), the simplest form of a NRTK system is a single-base RTK. In Australia there are several NRTK services operating in different states and over 1000 single-base RTK systems to support precise positioning applications for surveying, mining, agriculture, and civil construction in regional areas. Additionally, future generation GNSS constellations, including modernised GPS, Galileo, GLONASS, and Compass, with multiple frequencies have been either developed or will become fully operational in the next decade. A trend of future development of RTK systems is to make use of various isolated operating network and single-base RTK systems and multiple GNSS constellations for extended service coverage and improved performance. Several computational challenges have been identified for future NRTK services including: • Multiple GNSS constellations and multiple frequencies • Large scale, wide area NRTK services with a network of networks • Complex computation algorithms and processes • Greater part of positioning processes shifting from user end to network centre with the ability to cope with hundreds of simultaneous users’ requests (reverse RTK) There are two major requirements for NRTK data processing based on the four challenges faced by future NRTK systems, expandable computing power and scalable data sharing/transferring capability. This research explores new approaches to address these future NRTK challenges and requirements using the Grid Computing facility, in particular for large data processing burdens and complex computation algorithms. A Grid Computing based NRTK framework is proposed in this research, which is a layered framework consisting of: 1) Client layer with the form of Grid portal; 2) Service layer; 3) Execution layer. The user’s request is passed through these layers, and scheduled to different Grid nodes in the network infrastructure. A proof-of-concept demonstration for the proposed framework is performed in a five-node Grid environment at QUT and also Grid Australia. The Networked Transport of RTCM via Internet Protocol (Ntrip) open source software is adopted to download real-time RTCM data from multiple reference stations through the Internet, followed by job scheduling and simplified RTK computing. The system performance has been analysed and the results have preliminarily demonstrated the concepts and functionality of the new NRTK framework based on Grid Computing, whilst some aspects of the performance of the system are yet to be improved in future work.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

Fluid Mechanics of Aquatic Locomotion at Large Reynolds Numbers

Abstract | There exist a huge range of fish species besides other aquatic organisms like squids and salps that locomote in water at large Reynolds numbers, a regime of flow where inertial forces dominate viscous forces. In the present review, we discuss the fluid mechanics governing the locomotion of such organisms. Most fishes propel themselves by periodic undulatory motions of the body and tail, and the typical classification of their swimming modes is based on the fraction of their body that undergoes such undulatory motions. In the angulliform mode, or the eel type, the entire body undergoes undulatory motions in the form of a travelling wave that goes from head to tail, while in the other extreme case, the thunniform mode, only the rear tail (caudal fin) undergoes lateral oscillations. The thunniform mode of swimming is essentially based on the lift force generated by the airfoil like crosssection of the fish tail as it moves laterally through the water, while the anguilliform mode may be understood using the “reactive theory” of Lighthill. In pulsed jet propulsion, adopted by squids and salps, there are two components to the thrust; the first due to the familiar ejection of momentum and the other due to an over-pressure at the exit plane caused by the unsteadiness of the jet. The flow immediately downstream of the body in all three modes consists of vortex rings; the differentiating point being the vastly different orientations of the vortex rings. However, since all the bodies are self-propelling, the thrust force must be equal to the drag force (at steady speed), implying no net force on the body, and hence the wake or flow downstream must be momentumless. For such bodies, where there is no net force, it is difficult to directly define a propulsion efficiency, although it is possible to use some other very different measures like “cost of transportation” to broadly judge performance.