Numerical study of high-Reynolds number vortex flows with high-order accurate meshless vortex method.

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The flow of fluids is an unusually difficult subject to study, but it affects innumerable aspects of our life. The understanding of the flow of blood in the heart, the vortices created by jet airliners, the cooling of a laptop's microchip, and the flow of air in the atmosphere and water in the ocean, all of these require knowledge of fluid dynamics. Fluid dynamics is a very challenging and exciting field of science. The applications are countless, and so are the complexities. Because the general physical description of fluids results in a mathematical formulation --a differential equation-- which cannot in general be solved, scientists have attempted to use computer simulations since these were available. In fact, many advances in computational science are a direct result of the efforts to tackle some problem of fluid flow.Some flows are particularly difficult to solve, even with the most powerful computers. Flows involving eddies of multiple sizes, turbulence or rapid changes are the chief example. But vortices appear almost everywhere in fluids, and they are responsible for many phenomena that we would like to understand or control. For example, when we hear the noise of a helicopter, that noise is in great measure produced by the vortices left behind by one blade being hit by the next oncoming blade. And when airplanes are spaced by the control tower on approach to landing, it is mostly due to the need to avoid the vortices left behind by the previous plane landing. If our understanding of airplane vortices was such that we could predict where they are in a given moment, the instructions for the next oncoming plane could be safely given with airport efficiency in mind. A huge amount of money could be saved by increasing the frequency of landings in this way.To study these types of problems, the computational approach is essential. The field of Computational Fluid Dynamics involves computer simulations of problems of fluid flow. In this field, the majority of scientists use methods which are based on dividing the space where there is fluid into small elements, squares or triangles, or cubes, where the equations are said to be discretised. The equations are solved by, for example, keeping track of how much fluid enters one side, and leaves the other side, of the elements. These methods have been used for decades, and can produce excellent results. But many times they suffer from one problem: they diffuse the vortices too fast. Using again the example of the jet airliner, they would predict that the wake vortices are gone, when in fact they still persist and pose a danger to oncoming airplanes.Some computational scientists have been experimenting with different methods, where instead of using geometrical elements of fluid, a set of disconnected points are used to calculate the quantities of interest, like velocity. This field has come to be known as meshless or gridfree computation. The research of Dr Barba concentrates in this field, where the use of points, or fluid particles, results in calculations which are able to resolve the small eddies in the flows, and do not diffuse them too fast. The methods are in constant development, and recent advances mean that there is opportunity for very accurate simulations. The research programme of Barba aims to develop an advanced method, based on vortex particles, which is highly accurate. She will introduce innovations allowing the calculation of a range of scales in the flow, more efficiently, and develop clever ways of accounting for the presence of bodies immersed in the fluid. These advances promise to have a significant impact in the field of meshless computation. Moreover, she will use the new methods to study specific problems of interest to physical oceanographers and aerodynamicists, involving interaction of vortices. The results of this research will make progress in both vortex dynamics and computational science in general.