Flow feature detection for grid adaptation and flow visualization

Abstract Adaptive grid refinement/coarsening is an important method for achieving increased accuracy of flow simulations with reduced computing resources. Further, flow visualization of complex 3-D fields is a major task of both computational fluid dynamics (CFD), as well as experimental data analysis. A primary issue of adaptive simulations and flow visualization is the reliable detection of the local regions containing features of interest. A relatively wide spectrum of detection functions (sensors) is employed for representative flow cases which include boundary layers, vortices, jets, wakes, shock waves, contact discontinuities, and expansions. The focus is on relatively simple sensors based on local flow field variation using 3-D general hybrid grids consisting of multiple types of elements. A quantitative approach for sensors evaluation and comparison is proposed and applied. It is accomplished via the employment of analytic flow fields. Automation and effectiveness of an adaptive grid or flow visualization process requires the reliable determination of an appropriate threshold for the sensor. Statistical evaluation of the distributions of the sensors results in a proposed empirical formula for the threshold. The qualified sensors along with the automatic threshold determination are tested with more complex flow cases exhibiting multiple flow features.

[1]  Sophia Fotia,et al.  A priori mesh quality metrics for three-dimensional hybrid grids , 2015, J. Comput. Phys..

[2]  Angelo Casagrande Parallel mesh adaptive techniques for complex flow simulation , 2008 .

[3]  Kazuhiro Nakahashi,et al.  Output-Based Error Estimation and Adaptive Mesh Refinement Using Viscous Adjoint Method , 2006 .

[4]  Michel A. Saad,et al.  Compressible Fluid Flow , 1985 .

[5]  Robert Haimes,et al.  Shock detection from computational fluid dynamics results , 1999 .

[6]  Zi-Niu Wu,et al.  Review of shock wave detection method in CFD post-processing , 2013 .

[7]  Yannis Kallinderis,et al.  A new adaptive algorithm for turbulent flows , 1992 .

[8]  Lambertus Hesselink,et al.  Analysis and representation of complex structures in separated flows , 1991, Electronic Imaging.

[9]  Y. Kallinderis,et al.  Adaptation methods for a new Navier-Stokes algorithm , 1989 .

[10]  Y. Kallinderis,et al.  Quality Index and Improvement of the Interfaces of General Hybrid Grids , 2014 .

[11]  Kojiro Suzuki,et al.  Shock wave detection in two-dimensional flow based on the theory of characteristics from CFD data , 2011, J. Comput. Phys..

[12]  Yannis Kallinderis,et al.  Hybrid Grids and Their Applications , 1999 .

[13]  Raghu Machiraju,et al.  Vortex Visualization for Practical Engineering Applications , 2006, IEEE Transactions on Visualization and Computer Graphics.

[14]  Chris Henze,et al.  Feature Extraction of Separation and Attachment Lines , 1999, IEEE Trans. Vis. Comput. Graph..

[15]  Michael B. Giles,et al.  Adjoint Recovery of Superconvergent Functionals from PDE Approximations , 2000, SIAM Rev..

[16]  K. Pearson Mathematical contributions to the theory of evolution.—On the law of reversion , 2022, Proceedings of the Royal Society of London.

[17]  Y. Kallinderis Grid adaptation by redistribution and local embedding , 1996 .

[18]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[19]  Michael Andrew Park,et al.  Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation , 2004 .

[20]  Kazuhiro Nakahashi,et al.  Drag Decomposition-Based Adaptive Mesh Refinement , 2007 .

[21]  Raghu Machiraju,et al.  Boosting Techniques for Physics‐Based Vortex Detection , 2014, Comput. Graph. Forum.

[22]  Gerik Scheuermann,et al.  Topology-based Methods in Visualization , 2007, Topology-based Methods in Visualization.

[23]  Andrzej Herczynski,et al.  Two-fluid jets and wakes , 2004 .

[24]  Raghu Machiraju,et al.  Feature‐based adaptive mesh refinement for wingtip vortices , 2011 .

[25]  Yannis Kallinderis,et al.  A dynamic adaptation scheme for general 3-D hybrid meshes , 2005 .

[26]  Al Globus,et al.  A tool for visualizing the topology of three-dimensional vector fields , 1991, Proceeding Visualization '91.

[27]  M. Collins,et al.  Nursing Theories: The Base for Professional Nursing Practice, second ed., Julia B. George. Prentice-Hall, Inc, Englewood Cliffs, NJ 07632 (1985), 354, $15.95 paperback. , 1987 .

[28]  M. Sala,et al.  A parallel adaptive newton-krylov-schwarz method for 3D compressible inviscid flow simulations , 2013 .

[29]  Robert S. Laramee,et al.  The State of the Art , 2015 .

[30]  M. Fortin,et al.  Anisotropic mesh adaptation: towards user‐independent, mesh‐independent and solver‐independent CFD. Part I: general principles , 2000 .

[31]  E. Andrés,et al.  IMPLEMENTATION OF AN ADJOINT-BASED ERROR ESTIMATION AND GRID ADAPTATION MODULE IN THE DLR TAU CODE , 2010 .

[32]  John F. Dannenhoffer,et al.  Grid adaptation for the 2-D Euler equations , 1985 .

[33]  D. Venditti,et al.  Grid adaptation for functional outputs: application to two-dimensional inviscid flows , 2002 .

[34]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[35]  Sivakumaran Nadarajah,et al.  On the a Posteriori Error Estimation in Mesh Adaptation to Improve CFD Solutions , 2006 .

[36]  Holger Babinsky,et al.  Vortex Detection Methods for use with PIV and CFD data , 2009 .

[37]  MING JIANG,et al.  Detection and Visualization of Vortices , 2005, The Visualization Handbook.

[38]  Ralf Hartmann,et al.  Error estimation and adjoint-based adaptation in aerodynamics , 2006 .

[39]  Karl Pearson,et al.  Mathematical Contributions to the Theory of Evolution. XIX. Second Supplement to a Memoir on Skew Variation , 1901 .

[40]  David L. Marcum,et al.  SOLUTION ADAPTIVE UNSTRUCTURED GRID GENERATION USING PSEUDO-PATTERN RECOGNITION TECHNIQUES , 1997 .

[41]  Richard P. Dwight,et al.  Heuristic a posteriori estimation of error due to dissipation in finite volume schemes and application to mesh adaptation , 2008, J. Comput. Phys..

[42]  R. Haimes,et al.  On the velocity gradient tensor and fluid feature extraction , 1999 .

[43]  D. Thompson,et al.  Eduction of swirling structure using the velocity gradient tensor , 1991 .

[44]  John F. Dannenhoffer,et al.  Adaptive grid embedding Navier-Stokes technique for cascade flows , 1989 .

[45]  Raghu Machiraju,et al.  Geometric verification of swirling features in flow fields , 2002, IEEE Visualization, 2002. VIS 2002..

[46]  U. Rist,et al.  Enhanced Visualization of Late Stage Transitional Structures using Vortex Identi cation and Automatic Feature Extraction , 1998 .

[47]  Joseph E. Flaherty,et al.  An adaptive local mesh refinement method for time-dependent partial differential equations , 1989 .