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

流体的流动是一门非常难研究的学科，但它影响着我们生活的无数方面。了解心脏中的血液流动，喷气客机产生的漩涡，笔记本电脑微芯片的冷却，大气中的空气流动和海洋中的水，所有这些都需要流体动力学的知识。流体动力学是一个非常具有挑战性和令人兴奋的科学领域。应用程序是无数的，复杂性也是如此。由于流体的一般物理描述会产生一个通常无法求解的数学公式——微分方程，因此自计算机模拟出现以来，科学家们一直试图使用计算机模拟。事实上，计算科学的许多进步都是解决流体流动问题的直接结果。即使使用最强大的计算机，有些流程也特别难以解决。包括不同大小的漩涡、湍流或快速变化的流动是主要的例子。但是涡旋在流体中几乎无处不在，它们是许多我们想要理解或控制的现象的原因。例如，当我们听到直升机的噪音时，这种噪音在很大程度上是由一个叶片被另一个迎面而来的叶片撞击后留下的涡流产生的。当飞机在接近着陆时被控制塔隔开时，这主要是由于需要避免前一次飞机着陆留下的涡流。如果我们对飞机涡旋的理解是这样的，我们可以预测它们在给定时刻的位置，那么对下一架迎面而来的飞机的指示就可以在考虑机场效率的情况下安全地给出。通过这种方式增加着陆的频率可以节省大量的钱。为了研究这类问题，计算方法是必不可少的。计算流体动力学领域涉及流体流动问题的计算机模拟。在这个领域，大多数科学家使用的方法是基于将有流体的空间划分成小元素，正方形或三角形，或立方体，其中的方程被称为离散的。例如，通过记录有多少流体进入元素的一边，又有多少流体离开元素的另一边来求解这些方程。这些方法已经使用了几十年，并且可以产生很好的效果。但很多时候它们都有一个问题：它们扩散漩涡的速度太快了。再次以喷气式客机为例，他们会预测尾流漩涡已经消失，而实际上它们仍然存在，并对迎面而来的飞机构成危险。一些计算科学家一直在尝试不同的方法，他们不使用流体的几何元素，而是使用一组不相连的点来计算感兴趣的量，比如速度。这个领域被称为无网格计算或无网格计算。Barba博士的研究集中在这一领域，利用点或流体粒子，计算出能够解决气流中的小涡流，并且不会过快扩散的方法。这些方法在不断发展，最近的进展意味着有机会进行非常精确的模拟。Barba的研究计划旨在开发一种基于涡旋粒子的先进方法，该方法高度精确。她将引入一些创新，允许更有效地计算流体中的一系列尺度，并开发出一种聪明的方法来计算浸入流体中的物体的存在。这些进展有望在无网格计算领域产生重大影响。此外，她将使用新的方法来研究物理海洋学家和空气动力学家感兴趣的具体问题，包括涡旋的相互作用。这一研究成果将在涡旋动力学和计算科学领域取得广泛的进展。

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.