GPU and APU computations of Finite Time Lyapunov Exponent fields

We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.

[1]  Kyriakos C. Giannakoglou,et al.  CFD-based analysis and two-level aerodynamic optimization on Graphics Processing Units , 2010 .

[2]  Diego Rossinelli,et al.  GPU accelerated simulations of bluff body flows using vortex particle methods , 2010, J. Comput. Phys..

[3]  Michael Bergdorf,et al.  Multilevel Adaptive Particle Methods for Convection-Diffusion Equations , 2005, Multiscale Model. Simul..

[4]  Thomas M. Antonsen,et al.  Quasi-two-dimensional fast kinematic dynamo instabilities of chaotic fluid flows , 1996 .

[5]  John O Dabiri,et al.  The `upstream wake' of swimming and flying animals and its correlation with propulsive efficiency , 2008, Journal of Experimental Biology.

[6]  Boris Hasselblatt,et al.  Introduction to the Modern Theory of Dynamical Systems: PRINCIPAL CLASSES OF ASYMPTOTIC TOPOLOGICAL INVARIANTS , 1995 .

[7]  Samuel Williams,et al.  Roofline: an insightful visual performance model for multicore architectures , 2009, CACM.

[8]  George Haller,et al.  Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence , 2001 .

[9]  Petros Koumoutsakos,et al.  Simulations of single and multiple swimmers with non-divergence free deforming geometries , 2011, J. Comput. Phys..

[10]  Aaftab Munshi,et al.  The OpenCL specification , 2009, 2009 IEEE Hot Chips 21 Symposium (HCS).

[11]  Diego Rossinelli Multiresolution flow simulations on multi/many-core architectures , 2011 .

[12]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[13]  Inanc Senocak,et al.  CUDA Implementation of a Navier-Stokes Solver on Multi-GPU Desktop Platforms for Incompressible Flows , 2009 .

[14]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[15]  Thomas Peacock,et al.  Introduction to Focus Issue: Lagrangian Coherent Structures. , 2010, Chaos.

[16]  Graham Pullan,et al.  SBLOCK: A Framework for Efficient Stencil-Based PDE Solvers on Multi-core Platforms , 2010, 2010 10th IEEE International Conference on Computer and Information Technology.

[17]  Philippe Angot,et al.  A penalization method to take into account obstacles in incompressible viscous flows , 1999, Numerische Mathematik.

[18]  Hans Hagen,et al.  Visualization of Coherent Structures in Transient 2D Flows , 2009, Topology-Based Methods in Visualization II.

[19]  Arie E. Kaufman,et al.  Lattice-based flow field modeling , 2004, IEEE Transactions on Visualization and Computer Graphics.

[20]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[21]  Hans Hagen,et al.  Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications , 2007, IEEE Transactions on Visualization and Computer Graphics.

[22]  Diego Rossinelli,et al.  Mesh–particle interpolations on graphics processing units and multicore central processing units , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[23]  Graham Pullan,et al.  An Accelerated 3D Navier-Stokes Solver for Flows in Turbomachines , 2009 .

[24]  Satoshi Matsuoka,et al.  GPU accelerated computing—from hype to mainstream, the rebirth of vector computing , 2009 .

[25]  Jerrold E. Marsden,et al.  Transport and stirring induced by vortex formation , 2007, Journal of Fluid Mechanics.

[26]  George Haller,et al.  Predicting transport by Lagrangian coherent structures with a high-order method , 2006 .

[27]  Filip Sadlo,et al.  Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction , 2007, IEEE Transactions on Visualization and Computer Graphics.

[28]  G. Haller A variational theory of hyperbolic Lagrangian Coherent Structures , 2010 .

[29]  R. MacKay INTRODUCTION TO THE MODERN THEORY OF DYNAMICAL SYSTEMS (Encyclopaedia of Mathematics and its Applications 54) , 1997 .

[30]  Massimo Bernaschi,et al.  Graphics processing unit implementation of lattice Boltzmann models for flowing soft systems. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  John O Dabiri,et al.  Lagrangian coherent structures in low Reynolds number swimming , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[32]  P. Koumoutsakos MULTISCALE FLOW SIMULATIONS USING PARTICLES , 2005 .

[33]  Diego Rossinelli,et al.  Vortex methods for incompressible flow simulations on the GPU , 2008, The Visual Computer.

[34]  Eric Darve,et al.  Large calculation of the flow over a hypersonic vehicle using a GPU , 2008, J. Comput. Phys..

[35]  Steven L Brunton,et al.  Fast computation of finite-time Lyapunov exponent fields for unsteady flows. , 2010, Chaos.

[36]  George Haller,et al.  Optimal pollution mitigation in Monterey Bay based on coastal radar data and nonlinear dynamics. , 2007, Environmental science & technology.

[37]  G. Lapeyre,et al.  Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. , 2002, Chaos.

[38]  Graham Pullan,et al.  Acceleration of a 3D Euler solver using commodity graphics hardware , 2008 .

[39]  Mathieu Coquerelle,et al.  ARTICLE IN PRESS Available online at www.sciencedirect.com Journal of Computational Physics xxx (2008) xxx–xxx , 2022 .

[40]  Petros Koumoutsakos,et al.  Inviscid Axisymmetrization of an Elliptical Vortex , 1997 .

[41]  Arie E. Kaufman,et al.  Implementing lattice Boltzmann computation on graphics hardware , 2003, The Visual Computer.