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Position TitleIdentification of Lagrangian Coherent Structures (LCS) in accelerating turbulent boundary layers
SummaryIt is well known the crucial role of coherent structures (CS) in transporting momentum, energy and passive scalar fluxes. Significant effort has been invested in last two decades in terms of identifying and evaluating CS. The vortex identification Eulerian methods (such as Q, lambda_2 and lambda_ci methods) can effectively describe coherent features of the instantaneous flow fluid or passive scalar but lack objectivity. Haller and his colleagues have pioneered in the area of identifying and tracking CS by means of a Lagrangian approach, called Lagrangian Coherent Structures (LCS) [Ann. Rev. Fluid Mechanics, 47:137-162, 2015]. Due to this, the proposed approach of LCS will allow us to identify important structures in turbulent boundary layers subject to strong favorable pressure gradient (FPG) via a rigorous mathematical framework. The LCS approach is a cutting-edge CS identification technique with high level of precision. At the same time, LCS require high spatial/temporal resolution data with a consequent high computational cost. The main purpose of the BWSIP internship project will be to develop a post-processing code in CUDA platform and GPU capabilities in order to identify LCS (eigenvalues and eigenvectors) from a Direct Numerical Simulation (DNS) database.
Job DescriptionThe internship position is at the High Performance Computing and Visualization Lab (HPCVL) at the Dept. of Mechanical Engineering in the U. of Puerto Rico-Mayaguez (UPRM). The undergraduate student intern will work on a post-processing code in the area of CUDA platform programming with GPU capabilities to mitigate the performance issues. The principal objectives/tasks of this internship can be summarized as follows:
- Develop a C++ code for managing/reading a large database of Direct Numerical Simulation (DNS) related to incompressible spatially-developing turbulent boundary layers [1-3].
- Compute the corresponding Lyapunov exponents that describe dispersion characteristics in order to identify LCS, typically Finite Space Lyapunov Exponents (FSLEs) or Finite Time Lyapunov Exponents (FTLEs).
- Initially, these exponents will be obtained in different planes (2D). The second part of the project involves 3D computation of Lyapunov exponents, which will require GPU capabilities.

[1] Araya G., Castillo L. and Hussain F., The log behavior of the Reynolds shear stress in accelerating turbulent boundary layers, J. of Fluid Mechanics, Vol. 775, pp 189 – 200, 2015.
[2] Araya G. and Castillo L., DNS of turbulent thermal boundary layers subjected to adverse pressure gradients, Physics of Fluids, 25, 095107, 2013.
[3] Araya G., Castillo L., Meneveau C. and Jansen K., A dynamic multi-scale approach for turbulent inflow boundary conditions in spatially evolving flows, J. of Fluid Mechanics Vol. 670, pp. 581–605, 2011.
Use of Blue WatersAccess to the Blue Waters supercomputer will be crucial in the post-processing of high spatial/temporal resolution Direct Numerical Simulation (DNS) of turbulent boundary layers. A typical case contains 8-million points and approximately 1200 snapshots or timesteps. Therefore, GPU capabilities will be necessary in successfully tracking LCS in time. Numerical simulations contain the thermal field (temperature as a passive scalar), which can be used as a marker of the coherent structures, as well. Additionally, a disk space on the order of 8 TB will be requested for storage/analysis/visualization purposes of the resulting output.
Conditions/QualificationsThis internship position is opened for undergraduate students at the University of Puerto Rico-Mayaguez. Candidates should have basic knowledge on: C++ programming, Linux, fluid mechanics and turbulence. In addition, students should demonstrate willingness to learn CUDA programming and parallel computing. A skilled intern has already been identified.
Start Date03/01/2017
End Date02/28/2018
LocationMayaguez, Puerto Rico, Mechanical Engineering Dept., University of Puerto Rico-Mayaguez
Ernie Rivera