Highly efficient computation of Finite-Time Lyapunov Exponents (FTLE) on GPUs based on three-dimensional SPH datasets

• Published in: Computers & fluids Vol. 175; pp. 129 - 141
• Main Authors: Dauch, T.F., Rapp, T., Chaussonnet, G., Braun, S., Keller, M.C., Kaden, J., Koch, R., Dachsbacher, C., Bauer, H.-J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15.10.2018; Elsevier BV
• Subjects: Computational efficiency; Computational fluid dynamics; Computing time; CUDA; Datasets; Finite-Time Lyapunov Exponent; Fluid dynamics; Fluid flow; Fluid mechanics; FTLE; GPU; Lagrangian Coherent Structures; Liapunov exponents; Smooth particle hydrodynamics; Smoothed particle hydrodynamics; CUDA; Finite-Time Lyapunov Exponent; Smoothed particle hydrodynamics; 68; 35; FTLE; Lagrangian Coherent Structures; GPU; 76; 65
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2018.07.015

•Interactive evaluation of Finite-Time Lyapunov Exponents (FTLE) based on SPH results.•GPU optimized highly efficient code for FTLE evaluation in 2D and 3D.•FTLE-ridges of simulated vortex street in agreement with experimental findings (2D).•FTLE-ridges in vicinity of surface mounted cylinder reflect wake structure (3D). “Smoothed particle hydrodynamics” (SPH) is a particle method that becomes increasingly popular in different fields of science and engineering. Reason for the popularity are the different advantages in comparison to conventional grid-based computational fluid dynamics (CFD). One example is the much cheaper identification of ”Lagrangian coherent structures” (LCS) in fluid flows by means of the “finite-time Lyapunov exponent” (FTLE). Schemes for the evaluation of FTLE fields based on SPH datasets already exist. Despite the smaller computational effort required in case of SPH data, their evaluation is still costly. This may be the reason that no investigations have been published presently which address the application of existing schemes to SPH-data in 3-D. Therefore in the current paper a new and highly efficient GPU implementation of an existing scheme for the evaluation of FTLE fields is proposed that enables the interactive analysis of large SPH datasets. The suitability of the scheme in case of 3-D datasets and the computational efficiency of the novel GPU implementation are demonstrated. Furthemore, the so called particle birthtime is presented as a cheap alternative to FTLE fields, even though it has a variety of limitations compared to FTLE fields.