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Lorena Barba's Research page
Contact information: see my faculty profile.
Research Interests
I am a computational scientist and a fluid dynamicist. That is, I do research by means of computer simulations, I study and develop numerical methods, and the types of applications I am most interested in have to do with problems of fluid flow.
Big whorls and little whorls.
One of the challenges in fluid simulation continues to be the need to straddle many scales. New research in computational methods is still sorely needed to build schemes that are intelligent, detect the scales of the problem, and adapt. Moreover, we need programs that are hardware-aware.
A new-wave in computational fluid and solid mechanics is the development of meshfree methods. They promise to offer solutions to many enduring problems, such as dealing with discontinuities such as cracks and simulating flows with low numerical diffusion. I believe that, in addition, meshfree methods should be especially well-suited to exploit the new hardware technologies that are revolutionizing the scene. They should also more naturally offer ways to deal with multiple scales in a problem, and to construct adaptive schemes.
Meshfree methods also offer enormous potential for the simulation of problems involving moving and/or deformable boundaries, such as happens in most biological applications. In these problems, the need to adapt or regenerate a mesh is a huge burden for the computation and removing this burden will allow the solution of larger problems, in less time, and in smaller computers. Here, as in multi-scale problems, I believe we should also discover ways to combine continuum and particle approaches, hence build and test hybrid methods.
Research Group
- Dr Rio Yokota, postdoctoral researcher
- Rio obtained his PhD in July 2009 at Keio University, Japan. He works as a postdoctoral researcher now, funded by my EPSRC First Grant.
- Felipe Cruz, PhD student
- Felipe came to Bristol in November'06 funded by a mobility grant of the SCAT project. He worked on the implementation of the Fast Multipole Method (FMM) using the Python language, with which we have performed a suite of numerical experiments investigating the structure of the errors of the FMM applied to the vortex particle method. Since June 2007, Felipe is a PhD student, funded by a grant from BAE/Airbus to work on the development of hybrid particle-continuum methods and their implementation in novel computer architectures.
Past members
- Christopher Cooper, SCAT grantee
- Christopher was a visiting researcher funded by the SCAT project until November 2008. He worked on formulations of the boundary conditions when using vortex particle methods.
- Simon Layton, undergraduate student
- Simon worked on the implementation of the Fast Gauss Transform, for the fast calculation of the vorticity field, when it has been discretized by vortex particles.
- Justin Whalley, undergraduate student
- Justin studied the features of particle methods in regards to diffusive and dispersive numerical errors, as they compare with mainstream (grid-based) numerical methods.
- Dr Ross Bambrey, postdoctoral researcher
- Ross was in Bristol for a short six months, until he opted for a career switch. In that time, he investigated the use of wavelet analysis to detect scales in a flow, so as to refine particle representations of the vorticity field.
- Claudio Torres, SCAT grantee
- Claudio was a visiting researcher funded by the SCAT project. He worked on various topics, including a desingularized panel method, the simulation of a circular vortex sheet using the point vortex method and a block-method of solution of the field interpolation problem with Gaussians. Claudio has commenced PhD study in February 2008 at University of Delaware, under the supervision of my collaborator, Prof. Louis Rossi.
- Helmut Wahanik, SCAT grantee
- Helmut also came to Bristol funded by a mobility grant of the SCAT project. He worked on the implementation of a pseudo-spectral method for the calculation of vortical structures. Now, Helmut is doing PhD study at IMPA, Rio de Janeiro.
Various collaborations and projects
A graph of the spatial errors in an experiment with the fast multipole method. The colors map to a logarithmic scale, where blue is 1e-16 and red is 1e-9.
Fast methods for particle simulations
The fast multipole method was rated as one of the Top-10 algorithms of the 20th century, due to its dramatic impact on calculations of particle interactions with many particles. But one obstacle to a more widespread use is the algorithmic complexity and programming effort required to implement the method. With PhD student Felipe Cruz, we are developing an open source FMM implementation, whose first incarnation is a Python prototype. With this code, we have carried out a study of the errors of the FMM approximation, depending on the algorithm parameters.
Fluid Dynamics
I am interested in a variety of fundamental problems of fluid dynamics, such as high-Reynolds number flows with concentrated areas of vorticity and vortex dynamics in general. Applications of interest includy geophysical fluid dynamics, vortex-induced vibration, separated flows, moving boundaries, and many more.
Formation of a triangular vortex >> Paper PDF file
Owing to my incipient enthusiasm for the dynamics of the Earth's atmosphere and oceans, I have come to know and admire greatly the group at the Fluid Dynamics Laboratory in Eindhoven. Through a string of visits funded by the British Council-NWO Partnership Programme, I have had the pleasure of discussing fluids with Prof. Gert Jan van Heijst and collaborators, which has led to some new research ventures.
Coincidentally, I have recently begun a collaboration with Dr. Oscar Velasco Fuentes, who did his doctoral work at Eindhoven. Oscar and I met at the ICTAM Congress in 2004, and started corresponding; he visited Bristol in January 2006, and we are now working together to apply some concepts from dynamical systems to the study of coherent vortex structures. He was quite successful in applying these same ideas to clarifying the role of filamentation in the process of merging of vortices.
Vortex Particle Methods
I work with vortex particle methods and their applications for the computation of unsteady viscous flows. The state-of-the-art in vortex methods is represented by the work in the research groups of Prof. Gregoire Winckelmans in Louvain, Prof. Georges-Henri Cottet in Grenoble and Prof. Petros Koumoutsakos in Zurich. Petros has diversified in many more areas of computational science, including the cousin meshfree method SPH (smoothed particle hydrodynamics). Gregoire and his group, meanwhile, continue to impress the community with highly competitive applications of vortex methods in aerodynamics; for example, recent simulations of aircraft trailing vortices have surpassed every other method of CFD. Both Petros and Gregoire did their doctoral studies in Aeronautics at Caltech under Prof. Tony Leonard, who was also my PhD supervisor.
Although vortex methods are now well-established and competitive —as proved by the cumulative work of the scientists mentioned in the previous paragraph, and many others— we still attempt to introduce improvements and variations of implementation. Recently, Prof. Louis Rossi and myself have initiated a collaboration with the aim of demonstrating high-order vortex methods. The higher-order convergence is attained by combining elliptical basis functions, and spatial adaptation methods based on scattered data interpolation.
Meshfree Methods
In addition, I am interested in the development of the meshfree paradigm for computational methods, in general. The vortex particle method is (depending on the variant) a meshless method; there are also a variety of new methods being developed that do not rely on the construction of a mesh in the computational domain. This approach holds great promise to allow for computations of highly complex, unsteady flows, flows with moving boundaries, material problems with discontinuities (such as cracks), multi-scale computations, and many other extremely challenging problems.
The SCAT Project
SCAT stands for Scientific Computing Advanced Training, and it is a project co-financed by the ALFA Programme of the European Commission for collaboration with Latin America in science and technology. I put together a network of 10 institutions of higher education and research in Europe and Latin America, came up with the concept for this project, and wrote the proposal, which was successful at the 11th round of the programme, in October 2004. The project has brought together many scientists, organized international meetings and awarded mobility grants to graduate students and post-doctoral scholars in both continents.
Sample Research Topic
Emergence and evolution of vortex tripoles
When a strong vortex is subject to a perturbation, the first fundamental question that arises is whether it will return to an axisymmetric shape. In linear theory, it will. But when nonlinear effects are strong, structures like the tripole can emerge.