Abstract
As vortex is of great significance to structure analysis and mechanism research in flow field, vortex feature extraction has always been a hot research topic in flow field visualization. We investigate the data precision and numerical algorithm accuracy impact on vortex feature area extraction of Lagrangian Averaged Vorticity Deviation (LAVD). Then, an LAVD-based high-order accurate vortex extraction algorithm is proposed, which incorporates vorticity computation of cell-vertexed data by Weighted Essentially Non-Oscillatory (WENO) scheme, vorticity and velocity computation of off-grid point by candidate stencil weight-based high-order polynomial interpolation method, flow map computation by 4th-order Runge–Kutta (RK) method and integration by compound Simpson rule. We perform vortex feature extraction and visualization on both analytical flow field and high-order unsteady flow field. The experiment results demonstrate that the proposed algorithm can practically reflect the vortex feature of high-order flow field and accurately describe small scale vortex structure, which is unavailable by low-order method.
Graphical Abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beron-vera FJ, Wang Y, Olascoaga MJ, Goni JG, Haller G (2013) Objective detection of oceanic eddies and the Agulhas leakage. J Phys Oceanogr 43(7):1426–1438. doi:10.1175/jpo-d-12-0171.1
Chen C-M, Biswas A, Shen H-W (2015) Uncertainty modeling and error reduction for pathline computation in time-varying flow fields. IEEE Pac Vis Symp 2015:215–222. doi:10.1109/pacificvis.2015.7156380
Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three dimensional flow fields. Phys Fluids A 2(5):765–777. doi:10.1063/1.857730
Coppola G, Sherwin SJ, Peiró J (2001) Nonlinear particle tracking for high order elements. J Comput Phys 172(1):356–386. doi:10.1006/jcph.2001.6829
Coulliette C, Wiggins S (1999) Intergyre transport in a wind-driven, quasigeostrophic double gyre: an application of lobe dynamics. Nonlinear Processes Geophys 7(1/2):59–85. doi:10.5194/npg-7-59-2000
Froyland G (2012) An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D 250(5):1–19. doi:10.1016/j.physd.2013.01.013
Haller G (2001) Distinguished material surfaces and coherent structures in three dimensional fluid flows. Phisica D Nonlinear Phenom 149(4):248–277. doi:10.1016/s0167-2789(00)00199-8
Haller G (2005) An objective definition of a vortex. J Fluid Mech 525(1):1–26. doi:10.1017/s0022112004002526
Haller G, Beron-vera FJ (2012) Geodesic theory of transport barriers in two dimensional flows. Physica D 241(20):1680–1702. doi:10.1016/j.physd.2012.06.012
Haller G, Beron-vera FJ (2013) Coherent Lagrangian vortices: the black holes of turbulence. J Fluid Mech 731(3):134–140. doi:10.1017/jfm.2013.391
Haller G, Yuan G (2000) Lagrangian coherent structures and mixing in two dimensional turbulence. Physica D 147(34):352–370. doi:10.1016/s0167-2789(00)00142-1
Haller G, Hadjighasem A, Farazmand M, Huhn F (2016) Defining coherent vortices objectively from the vorticity. J Fluid Mech 795(2016):136–173. doi:10.1017/jfm.2016.151
Hunt JCR, Wray AA, Moin P (1988) Eddies, streams, convergence zones in turbulent flows. Cent Turbul Res 1:193–208
Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285(4):69–94
Jiang G-S, Shu C-W (1996) Efficient implementation of weighted ENO schemes. J Comput Phys 126(1):202–228. doi:10.1006/jcph.1996.0130
Leung S-Y (2011) An Eulerian approach for computing the finite time Lyapunov exponent. J Comput Phys 230(9):3500–3524. doi:10.1016/j.jcp.2011.01.046
Lugt HJ (1979) The dilemma of defining a vortex. Recent developments in theoretical and experimental fluid mechanics. Springer, Berlin, pp 309–321. doi:10.1007/978-3-642-67220-0_32
Ma T, Bollt E (2014) Differential geometry perspective of shape coherence and curvature evolution by finite-time non-hyperbolic splitting. J Appl Dyn Syst 13(3):1106–1136. doi:10.1137/130940633
Ma Q-L, Xu H-X, Zeng L, Cai X, Li S-K (2010) Direct raycasting of unstructured cell-centered data by discontinuity Roe-average computation. Vis Comput 26(6–8):1049–1059. doi:10.1007/s00371-010-0447-9
Nelson DA, Jacobs GB (2015) DG-FTLE: lagrangian coherent structures with high-order discontinuous-Galerkin methods. J Comput Phys 295:65–86. doi:10.1016/j.jcp.2015.03.040
Nelson B, Kirby RM (2006) Ray-tracing polymorphic multidomain spectral/hp elements for isosurface rendering. IEEE Trans Vis Comput Graphics 12(1):114–125. doi:10.1109/tvcg.2006.12
Nelson B, Liu E, Kirby RM, Haimes R (2012) ElVis: a system for the accurate and interactive visualization of high order finite element solutions. IEEE Trans Vis Comput Gr 18(12):2325–2334. doi:10.1109/tvcg.2012.218
Peacock T, Froyland G, Haller G (2015) Introduction to focus issue: objective detection of coherent structures. Chaos Interdiscip J Nonlinear Sci. doi:10.1063/1.4928894
Scandaliato AL, Liou M-S (2010) AUSM-based high-order solution for euler equations. Commun Comput Phys 12(4):1096–1120. doi:10.4208/cicp.250311.081211a
Shadden SC, Lekienb F, Marsdena JE (2005) Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two dimensional aperiodic flows. Phis D Nonlinear Phenom 212(3–4):271–304. doi:10.1016/j.physd.2005.10.007
Steffen M, Curtis S, Kirby RM, Ryan JK (2008) Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields. IEEE Trans Vis Comput Gr 14(3):680–692. doi:10.1109/tvcg.2008.9
Tsoutsanis P, Antoniadis AF, Drikakis D (2014) WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows. J Comput Phys 256(1):254–276. doi:10.1016/j.jcp.2013.09.002
Walfisch D, Ryan JK, Kirby RM, Haimes R (2009) One-sided smoothness-increasing accuracy-conserving filtering for enhanced streamline integration through discontinuous Fields. J Sci Comput 38(2):164–184. doi:10.1007/s10915-008-9230-8
Zhang L-P, Liu W, He L-X, Deng X-G, Zhang H-X (2012a) A class of hybrid DG/FV methods for conservation laws I: basic formulation and one-dimensional systems. J Comput Phys 231(4):1081–1103. doi:10.1016/j.jcp.2011.06.010
Zhang L-P, Liu W, He L-X, Deng X-G, Zhang H-X (2012b) A class of hybrid DG/FV methods for conservation laws II: two-dimensional cases. J Comput Phys 231(4):1104–1120. doi:10.1016/j.jcp.2011.03.032
Acknowledgements
This work is supported by the National Key Research and Development Program of China (2016YFB0200701), Chinese 973 Program (2015CB-755604), and the National Natural Science Foundation of China (61202335).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, F., Zhao, D., Deng, L. et al. An accurate vortex feature extraction method for Lagrangian vortex visualization on high-order flow field data. J Vis 20, 729–742 (2017). https://doi.org/10.1007/s12650-017-0421-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12650-017-0421-y