36,897 research outputs found
Fourth-order flows in surface modelling
This short article is a brief account of the usage of fourth-order curvature
flow in surface modelling
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
Numerical studies of the fluid and optical fields associated with complex cavity flows
Numerical solutions for the flowfield about several cavity configurations have been computed using the Reynolds averaged Navier-Stokes equations. Comparisons between numerical and experimental results are made in two dimensions for free shear layers and a rectangular cavity, and in three dimensions for the transonic aero-window problem of the Stratospheric Observatory for Infrared Astronomy (SOFIA). Results show that dominant acoustic frequencies and magnitudes of the self excited resonant cavity flows compare well with the experiment. In addition, solution sensitivity to artificial dissipation and grid resolution levels are determined. Optical path distortion due to the flow field is modelled geometrically and is found to match the experiment. The fluid field was computed using a diagonalized scheme within an overset mesh framework. An existing code, OVERFLOW, was utilized with the additions of characteristic boundary condition and output routines required for reduction of the unsteady data. The newly developed code is directly applicable to a generalized three dimensional structured grid zone. Details are provided in a paper included in Appendix A
Turbulence and passive scalar transport in a free-slip surface
We consider the two-dimensional (2D) flow in a flat free-slip surface that
bounds a three-dimensional (3D) volume in which the flow is turbulent. The
equations of motion for the two-dimensional flow in the surface are neither
compressible nor incompressible but strongly influenced by the 3D flow
underneath the surface. The velocity correlation functions in the 2D surface
and in the 3D volume scale with the same exponents. In the viscous subrange the
amplitudes are the same, but in the inertial subrange the 2D one is reduced to
2/3 of the 3D amplitude. The surface flow is more strongly intermittent than
the 3D volume flow. Geometric scaling theory is used to derive a relation
between the scaling of the velocity field and the density fluctuations of a
passive scalar advected on the surface.Comment: 11 pages, 10 Postscript figure
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Simulating Tsunami Inundation and Soil Response in a Large Centrifuge.
Tsunamis are rare, extreme events and cause significant damage to coastal infrastructure, which is often exacerbated by soil instability surrounding the structures. Simulating tsunamis in a laboratory setting is important to further understand soil instability induced by tsunami inundation processes. Laboratory simulations are difficult because the scale of such processes is very large, hence dynamic similitude cannot be achieved for small-scale models in traditional water-wave-tank facilities. The ability to control the body force in a centrifuge environment considerably reduces the mismatch in dynamic similitude. We review dynamic similitudes under a centrifuge condition for a fluid domain and a soil domain. A novel centrifuge apparatus specifically designed for exploring the physics of a tsunami-like flow on a soil bed is used to perform experiments. The present 1:40 model represents the equivalent geometric scale of a prototype soil field of 9.6 m deep, 21 m long, and 14.6 m wide. A laboratory facility capable of creating such conditions under the normal gravitational condition does not exist. With the use of a centrifuge, we are now able to simulate and measure tsunami-like loading with sufficiently high water pressure and flow velocities. The pressures and flow velocities in the model are identical to those of the prototype yielding realistic conditions of flow-soil interaction
Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments
A spectrogram of a ship wake is a heat map that visualises the time-dependent
frequency spectrum of surface height measurements taken at a single point as
the ship travels by. Spectrograms are easy to compute and, if properly
interpreted, have the potential to provide crucial information about various
properties of the ship in question. Here we use geometrical arguments and
analysis of an idealised mathematical model to identify features of
spectrograms, concentrating on the effects of a finite-depth channel. Our
results depend heavily on whether the flow regime is subcritical or
supercritical. To support our theoretical predictions, we compare with data
taken from experiments we conducted in a model test basin using a variety of
realistic ship hulls. Finally, we note that vessels with a high aspect ratio
appear to produce spectrogram data that contains periodic patterns. We can
reproduce this behaviour in our mathematical model by using a so-called
two-point wavemaker. These results highlight the role of wave interference
effects in spectrograms of ship wakes.Comment: 14 pages, 7 figure
Local movement: agent-based models of pedestrian flows
Modelling movement within the built environment has hitherto been focused on rather coarse spatial scales where the emphasis has been upon simulating flows of traffic between origins and destinations. Models of pedestrian movement have been sporadic, based largely on finding statistical relationships between volumes and the accessibility of streets, with no sustained efforts at improving such theories. The development of object-orientated computing and agent-based models which have followed in this wake, promise to change this picture radically. It is now possible to develop models simulating the geometric motion of individual agents in small-scale environments using theories of traffic flow to underpin their logic. In this paper, we outline such a model which we adapt to simulate flows of pedestrians between fixed points of entry - gateways - into complex environments such as city centres, and points of attraction based on the location of retail and leisure facilities which represent the focus of such movements. The model simulates the movement of each individual in terms of five components; these are based on motion in the direction of the most attractive locations, forward movement, the avoidance of local geometric obstacles, thresholds which constrain congestion, and movement which is influenced by those already moving towards various locations. The model has elements which enable walkers to self-organise as well as learn from their geometric experiences so far. We first outline the structure of the model, present a computable form, and illustrate how it can be programmed as a variant of cellular automata. We illustrate it using three examples: its application to an idealised mall where we show how two key components - local navigation of obstacles and movement towards points of global locational attraction - can be parameterised, an application to the more complex town centre of Wolverhampton (in the UK West Midlands) where the paths of individual walkers are used to explore the veracity of the model, and finally it application to the Tate Gallery complex in central London where the focus is on calibrating the model by letting individual agents learn from their experience of walking within the environment
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