“Building a Virtual Weakly-Compressible Wind Tunnel Testing Facility” by Lyu, Bai, Wu, Desbrun, Zheng, et al. …
Conference:
Type:
Title:
- Building a Virtual Weakly-Compressible Wind Tunnel Testing Facility
Session/Category Title: Going With The Flow
Presenter(s)/Author(s):
Moderator(s):
Abstract:
Virtual wind tunnel testing is a key ingredient in the engineering design process for the automotive and aeronautical industries as well as for urban planning: through visualization and analysis of the simulation data, it helps optimize lift and drag coefficients, increase peak speed, detect high pressure zones, and reduce wind noise at low cost prior to manufacturing. In this paper, we develop an efficient and accurate virtual wind tunnel system based on recent contributions from both computer graphics and computational fluid dynamics in high-performance kinetic solvers. Running on one or multiple GPUs, our massively-parallel lattice Boltzmann model meets industry standards for accuracy and consistency while exceeding current mainstream industrial solutions in terms of efficiency — especially for unsteady turbulent flow simulation at very high Reynolds number (on the order of 107) — due to key contributions in improved collision modeling and boundary treatment, automatic construction of multiresolution grids for complex models, as well as performance optimization. We demonstrate the efficacy and reliability of our virtual wind tunnel testing facility through comparisons of our results to multiple benchmark tests, showing an increase in both accuracy and efficiency compared to state-of-the-art industrial solutions. We also illustrate the fine turbulence structures that our system can capture, indicating the relevance of our solver for both VFX and industrial product design.
References:
1. Bart Adams, Mark Pauly, Richard Keiser, and Leonidas J. Guibas. 2007. Adaptively Sampled Particle Fluids. In ACM SIGGRAPH 2007 Papers. 48.
2. Ronojoy Adhikari and Sauro Succi. 2008. Duality in Matrix Lattice Boltzmann Models. Phys. Rev. E 78 (2008), 066701. Issue 6.
3. Giancarlo Alfonsi. 2009. Reynolds-Averaged Navier-Stokes Equations for Turbulence Modeling. Applied Mechanics Reviews 62, 4 (2009).
4. Alexis Angelidis and Fabrice Neyret. 2005. Simulation of Smoke Based on Vortex Filament Primitives. In Symposium on Computer Animation. 87–96.
5. Sandosh Ansumali, Ilya V. Karlin, and Hans C. Öttinger. 2003. Minimal Entropic Kinetic Models for Hydrodynamics. Europhysics Letters (EPL) 63, 6 (2003), 798–804.
6. Katsumi Aoki, Koji Muto, and Hiroo Okanaga. 2010. Aerodynamic characteristics and flow pattern of a golf ball with rotation. Procedia Engineering 2, 2 (2010), 2431–2436. The Engineering of Sport 8 – Engineering Emotion.
7. Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, and Pierre Sagaut. 2021. Lattice Boltzmann Method for Computational Aeroacoustics on Non-uniform Meshes: a direct grid coupling approach. J. Comp. Phys. 447 (2021), 110667.
8. Matthew Aultman, Rodrigo Auza-Gutierrez, Kevin Disotell, and Lian Duan. 2022. Effects of Wheel Rotation on Long-Period Wake Dynamics of the DrivAer Fastback Model. Fluids 7, 1 (2022).
9. Peter Bailey, Joe Myre, Stuart D.C. Walsh, David J. Lilja, and Martin O. Saar. 2009. Accelerating Lattice Boltzmann Fluid Flow Simulations Using Graphics Processors. In 2009 International Conference on Parallel Processing. 550–557.
10. Reza Barati, Seyed Ali Akbar Salehi Neyshabouri, and Goodarz Ahmadi. 2014. Development of empirical models with high accuracy for estimation of drag coefficient of flow around a smooth sphere: An evolutionary approach. Powder Technology 257 (2014), 11–19.
11. Peter W. Bearman and John K. Harvey. 1976. Golf Ball Aerodynamics. Aeronautical Quarterly 27, 2 (1976), 112–122.
12. Markus Becker and Matthias Teschner. 2007. Weakly Compressible SPH for Free Surface Flows. In Symposium on Computer Animation. 209–217.
13. Jan Bender and Dan Koschier. 2015. Divergence-Free Smoothed Particle Hydrodynamics. In Symposium on Computer Animation. 147–155.
14. M’hamed Bouzidi, Mouaouia Firdaouss, and Pierre Lallemand. 2001. Momentum Transfer of a Lattice-Boltzmann Fluid with Boundaries. Physics of Fluids 13, 11 (2001), 3452–3459.
15. Jeremiah U. Brackbill and Hans M. Ruppel. 1986. FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. J. Comput. Phys. 65, 2 (1986), 314–343.
16. John R. Chawner and Nigel J. Taylor. 2019. Progress in Geometry Modeling and Mesh Generation Toward the CFD Vision 2030. 2945.
17. Hudong Chen, Olga Filippova, James Hoch, Kim Molvig, Richard Shock, Christopher Teixeira, and Raoyang Zhang. 2006. Grid Refinement in Lattice Boltzmann Methods Based on Volumetric Formulation. Physica A: Statistical Mechanics and its Applications 362, 1 (2006), 158–167.
18. Hudong Chen, Pradeep Gopalakrishnan, and Raoyang Zhang. 2014. Recovery of Galilean Ivariance in Thermal Lattice Boltzmann Models for Arbitrary Prandtl Number. International Journal of Modern Physics C 25, 10 (2014), 1450046.
19. Li Chen, Yang Yu, and Guoxiang Hou. 2013. Sharp-interface Immersed Boundary Lattice Boltzmann Method with Reduced Spurious-pressure Oscillations for Moving Boundaries. Physical Review E 87, 5 (2013), 053306.
20. Shiyi Chen and Gary D Doolen. 1998. Lattice Boltzmann Method for Fluid Flows. Annual Review of Fluid Mechanics 30, 1 (1998), 329–364.
21. Yixin Chen, Wei Li, Rui Fan, and Xiaopei Liu. 2022. GPU Optimization for High-Quality Kinetic Fluid Simulation. IEEE Trans. Vis. Comp. Graph. 28, 9 (2022), 3235–3251.
22. Yong Chen, Xiangyang Wang, and Hanhua Zhu. 2021. A General Single-node Second-order Boundary Condition for the Lattice Boltzmann Method. Physics of Fluids 33, 4 (2021), 043317.
23. Nuttapong Chentanez and Matthias Müller. 2014. Mass-Conserving Eulerian Liquid Simulation. IEEE Trans. Vis. Comput. Graph. 20, 1 (2014), 17–29.
24. Byoungjin Chun and Anthony J.C. Ladd. 2007. Interpolated Boundary Condition for Lattice Boltzmann Simulations of Flows in Narrow Gaps. Physical Review E 75, 6 (2007), 066705.
25. Christophe Coreixas, Gauthier Wissocq, Guillaume Puigt, Jean-François Boussuge, and Pierre Sagaut. 2017. Recursive Regularization Step for High-order Lattice Boltzmann Methods. Phys. Rev. E 96 (2017), 033306. Issue 3.
26. Paul J. Dellar. 2001. Bulk and shear viscosities in lattice Boltzmann equations. Phys. Rev. E 64 (2001), 031203. Issue 3.
27. Mathieu Desbrun and Marie-Paule Gascuel. 1996. Smoothed particles: A new paradigm for animating highly deformable bodies. In Comp. Anim. & Simul. 61–76.
28. Rahul Deshpande, Vivek Kanti, Aditya Desai, and Sanjay Mittal. 2017. Intermittency of laminar separation bubble on a sphere during drag crisis. Journal of Fluid Mechanics 812 (2017), 815–840.
29. Dominique D’Humières. 1992. Generalized Lattice-Boltzmann Equations. In Rarefied Gas Dynamics: Theory and Simulations. 450–458.
30. Dominique D’Humières, Irina Ginzburg, Manfred Krafczyk, Pierre Lallemand, and Li-Shi Luo. 2002. Multiple-relaxation-time Lattice Boltzmann Models in Three Dimensions. Phil. Trans. R. Soc. A: Math. Phys. Eng. Sci. 360, 1792 (2002), 437–451.
31. Alexandre Dupuis and Bastien Chopard. 2003. Theory and Applications of an Alternative Lattice Boltzmann Grid Refinement Algorithm. Phys. Rev. E 67 (2003), 066707. Issue 6.
32. Jack G.M. Eggels. 1996. Direct and Large-eddy Simulation of Turbulent Fluid Flow using the Lattice-Boltzmann Scheme. International Journal of Heat and Fluid Flow 17, 3 (1996), 307–323.
33. Georg Eitel-Amor, Matthias Meinke, and Wolfgang Schröder. 2013. A lattice-Boltzmann method with hierarchically refined meshes. Computers & Fluids 75 (2013), 127–139.
34. Exa/3DS. 2023. SIMULIA PowerFLOW. Dassault Systèmes.
35. Robert Eymard, Thierry Gallouët, and Raphaèle Herbin. 2000. Finite volume methods. In Solution of Equation in Rn (Part 3), Techniques of Scientific Computing (Part 3). Handbook of Numerical Analysis, Vol. 7. Elsevier, 713–1018.
36. Yun (Raymond) Fei, Qi Guo, Rundong Wu, Li Huang, and Ming Gao. 2021. Revisiting Integration in the Material Point Method: A Scheme for Easier Separation and Less Dissipation. ACM Trans. Graph. 40, 4, Article 109 (2021).
37. Joel H. Ferziger, Milovan Perić, and Robert L Street. 2002. Computational methods for fluid dynamics. Vol. 3. Springer.
38. Olga Filippova and Dieter Hänel. 1998. Grid Refinement for Lattice-BGK Models. J. Comp. Phys. 147, 1 (1998), 219–228.
39. Nick Foster and Dimitri Metaxas. 1996. Realistic Animation of Liquids. Graphical Models and Image Processing 58, 5 (1996), 471–483.
40. Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, and Joseph Teran. 2017. A Polynomial Particle-in-Cell Method. ACM Trans. Graph. 36, 6, Article 222 (2017).
41. Martin Geier, Andreas Greiner, and Jan G. Korvink. 2006. Cascaded Digital Lattice Boltzmann Automata for High Reynolds Number Flow. Phys. Rev. E 73 (2006), 066705. Issue 6.
42. Martin Geier, Andreas Greiner, and Jan G. Korvink. 2009. A Factorized Central Moment Lattice Boltzmann Method. The European Physical Journal Special Topics 171, 1 (2009), 55–61.
43. Martin Geier, Andrea Pasquali, and Martin Schönherr. 2017a. Parametrization of the Cumulant Lattice Boltzmann Method for Fourth Order Accurate Diffusion Part I: derivation and validation. J. Comp. Phys. 348 (2017), 862–888.
44. Martin Geier, Andrea Pasquali, and Martin Schönherr. 2017b. Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion part II: Application to flow around a sphere at drag crisis. J. Comput. Phys. 348 (2017), 889–898.
45. Martin Geier and Martin Schönherr. 2017. Esoteric Twist: An Efficient in-Place Streaming Algorithmus for the Lattice Boltzmann Method on Massively Parallel Hardware. Computation 5, 2 (2017).
46. Martin Geier, Martin Schönherr, Andrea Pasquali, and Manfred Krafczyk. 2015. The Cumulant Lattice Boltzmann Equation in Three Dimensions: theory and validation. Computers & Mathematics with Applications 70, 4 (2015), 507–547.
47. Félix Gendre, Denis Ricot, Guillaume Fritz, and Pierre Sagaut. 2017. Grid refinement for aeroacoustics in the lattice Boltzmann method: A directional splitting approach. Phys. Rev. E 96 (2017), 023311. Issue 2.
48. Irina Ginzburg and Dominique D’Humières. 2003. Multireflection Boundary Conditions for Lattice Boltzmann Models. Phys. Rev. E 68 (2003), 066614. Issue 6.
49. Ehsan Goraki Fard. 2015. Cumulant LBM approach for Large Eddy Simulation of Dispersion Microsystems. Ph. D. Dissertation. Technische Universität Braunschweig.
50. Joseph L. Greathouse and Mayank Daga. 2014. Efficient Sparse Matrix-Vector Multiplication on GPUs Using the CSR Storage Format. In SC ’14: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. 769–780.
51. Francis H Harlow. 1962. The particle-in-cell method for numerical solution of problems in fluid dynamics. Technical Report. Los Alamos National Lab, USA.
52. Manuel Hasert, Kannan Masilamani, Simon Zimny, Harald Klimach, Jiaxing Qi, Jörg Bernsdorf, and Sabine Roller. 2014. Complex Fluid Simulations with the Parallel Tree-based Lattice Boltzmann Solver Musubi. J. Comp. Sci. 5, 5 (2014), 784–794.
53. Angelina Heft, Thomas Indinger, and Nikolaus Adams. 2011. Investigation of Unsteady Flow Structures in the Wake of a Realistic Generic Car Model.
54. Angelina I. Heft, Thomas Indinger, and Nikolaus A. Adams. 2012a. Experimental and Numerical Investigation of the DrivAer Model (Fluids Engineering Division Summer Meeting, Vol. Volume 1: Symposia, Parts A and B). American Society of Mechanical Engineers, 41–51.
55. Angelina I Heft, Thomas Indinger, and Nikolaus A Adams. 2012b. Introduction of a new realistic generic car model for aerodynamic investigations. Technical Report. SAE Technical Paper.
56. Shuling Hou, James Sterling, Shiyi Chen, and Gary D. Doolen. 1994. A Lattice Boltzmann Subgrid Model for High Reynolds Number Flows. arXiv:comp-gas/9401004.
57. Yu Hou, David Angland, Alois Sengissen, and Aline Scotto. 2019. Lattice-Boltzmann and Navier-Stokes simulations of the partially dressed, cavity-closed nose landing gear benchmark case. In 25th AIAA/CEAS aeroacoustics conference. 2555.
58. Markus Ihmsen, Jens Cornelis, Barbara Solenthaler, Christopher Horvath, and Matthias Teschner. 2014a. Implicit Incompressible SPH. IEEE Trans. Vis. Comput. Graph. 20, 3 (2014), 426–435.
59. Markus Ihmsen, Jens Orthmann, Barbara Solenthaler, Andreas Kolb, and Matthias Teschner. 2014b. SPH Fluids in Computer Graphics. In Eurographics – State of the Art Reports, Sylvain Lefebvre and Michela Spagnuolo (Eds.).
60. Martin Imre, Jun Tao, and Chaoli Wang. 2017. Efficient GPU-accelerated computation of isosurface similarity maps. In 2017 IEEE Pacific Visualization Symposium. 180–184.
61. Peter Irwin, Roy Denoon, and David Scott. 2013. Wind Tunnel Testing of High-Rise Buildings. Routledge.
62. Jérôme Jacob, Orestis Malaspinas, and Pierre Sagaut. 2018. A New Hybrid Recursive Regularised Bhatnagar-Gross-Krook Collision Model for Lattice Boltzmann Method-based Large Eddy Simulation. Journal of Turbulence 19, 11–12 (2018), 1051–1076.
63. Taryn James, Neil Lewington, Lothar Krueger, Manfred Lentzen, Karel Chalupa, Burkhard Hupertz, and Sudesh Woodiga. 2018. Development and Initial Testing of a Full-Scale DrivAer Generic Realistic Wind Tunnel Correlation and Calibration Model. SAE Int. J. Passenger Cars-Mechanical Systems 11, 5 (2018), 353–368.
64. Hrvoje Jasak and Tessa Uroić. 2020. Practical computational fluid dynamics with the finite volume method. In Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids. Springer, 103–161.
65. Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. 2015. The Affine Particle-in-Cell Method. ACM Trans. Graph. 34, 4, Article 51 (2015).
66. Shin K Kang and Yassin A Hassan. 2011. A comparative study of direct-forcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries. International Journal for Numerical Methods in Fluids 66, 9 (2011), 1132–1158.
67. I. V. Karlin, F. Bösch, and S. S. Chikatamarla. 2014. Gibbs’ Principle for the Lattice-kinetic Theory of Fluid Dynamics. Phys. Rev. E 90 (2014), 031302. Issue 3.
68. I. V. Karlin, A. Ferrante, and H. C. Öttinger. 1999. Perfect Entropy Functions of the Lattice Boltzmann Method. Europhysics Letters (EPL) 47, 2 (1999), 182–188.
69. Tero Karras. 2012. Maximizing Parallelism in the Construction of BVHs, Octrees, and k-d Trees. In Proceedings of the ACM SIGGRAPH / Eurographics Conference on High-Performance Graphics. 33–37.
70. ByungMoon Kim, Yingjie Liu, Ignacio Llamas, and Jarek Rossignac. 2005. FlowFixer: Using BFECC for Fluid Simulation. In Eurographics Workshop on Natural Phenomena.
71. Manfred Krafczyk, Jonas Tölke, and Li-Shi Luo. 2003. Large-eddy simulations with a multiple-relaxation-time LBE model. International Journal of Modern Physics B 17, 01–02 (2003), 33–39.
72. Andreas Krämer, Dominik Wilde, Knut Küllmer, Dirk Reith, and Holger Foysi. 2019. Pseudoentropic derivation of the regularized lattice Boltzmann method. Phys. Rev. E 100 (2019), 023302. Issue 2.
73. Timm Krüger, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, Goncalo Silva, and Erlen M. Viggen. 2016. The Lattice Boltzmann Method: Principles and Practice. Springer.
74. Adrian Kummerländer, Márcio Dorn, Martin Frank, and Mathias J. Krause. 2023. Implicit propagation of directly addressed grids in lattice Boltzmann methods. Concurrency and Computation: Practice and Experience 35, 8 (2023), e7509.
75. Anthony J. C. Ladd. 1994. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. Journal of Fluid Mechanics 271 (1994), 285–309.
76. Daniel Lagrava. 2012. Revisiting grid refinement algorithms for the lattice Boltzmann method. Ph. D. Dissertation. Université de Genève.
77. Daniel Lagrava, Orestis Malaspinas, Jonas Lätt, and Bastien Chopard. 2012. Advances in Multi-domain Lattice Boltzmann Grid Refinement. J. Comp. Phys. 231, 14 (2012), 4808–4822.
78. Pierre Lallemand and Li-Shi Luo. 2000. Theory of the Lattice Boltzmann Method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61 (2000), 6546–6562. Issue 6.
79. Pierre Lallemand, Li-Shi Luo, Manfred Krafczyk, and Wen-An Yong. 2021. The lattice Boltzmann method for nearly incompressible flows. J. Comp. Phys. 431 (2021), 109713.
80. Jonas Lätt and Bastien Chopard. 2006. Lattice Boltzmann Method with Regularized Pre-collision Distribution Functions. Mathematics and Computers in Simulation 72, 2 (2006), 165–168.
81. Jonas Lätt, Orestis Malaspinas, Dimitrios Kontaxakis, Andrea Parmigiani, Daniel Lagrava, Federico Brogi, Mohamed Ben Belgacem, Yann Thorimbert, Sébastien Leclaire, Sha Li, Francesco Marson, Jonathan Lemus, Christos Kotsalos, Raphaël Conradin, Christophe Coreixas, Rémy Petkantchin, Franck Raynaud, Joël Beny, and Bastien Chopard. 2021. Palabos: Parallel Lattice Boltzmann Solver. Computers & Mathematics with Applications 81 (2021), 334–350.
82. Sylvain Lefebvre and Hugues Hoppe. 2006. Perfect Spatial Hashing. ACM Trans. Graph. 25, 3 (2006), 579–588.
83. Moritz Lehmann. 2022. Esoteric Pull and Esoteric Push: Two Simple In-Place Streaming Schemes for the Lattice Boltzmann Method on GPUs. Computation 10, 6 (2022).
84. Wei Li, Kai Bai, and Xiaopei Liu. 2019. Continuous-Scale Kinetic Fluid Simulation. IEEE Trans. Vis. Comput. Graph. 25, 9 (2019), 2694–2709.
85. Wei Li, Yixin Chen, Mathieu Desbrun, Changxi Zheng, and Xiaopei Liu. 2020. Fast and Scalable Turbulent Flow Simulation with Two-Way Coupling. ACM Trans. Graph. 39, 4 (2020).
86. Wei Li and Mathieu Desbrun. 2023. Fluid-Solid Coupling in Kinetic Two-Phase Flow Simulation. ACM Trans. Graph. 42, 4, Article XXX (2023).
87. Wei Li, Yihui Ma, Xiaopei Liu, and Mathieu Desbrun. 2022. Efficient Kinetic Simulation of Two-Phase Flows. ACM Trans. Graph. 41, 4, Article 114 (2022), 17 pages.
88. Zhe Li, Julien Favier, Umberto D’Ortona, and Sébastien Poncet. 2016. An Immersed Boundary-lattice Boltzmann Method for Single- and Multi-component Fluid Flows. J. Comp. Phys. 304 (2016), 424–440.
89. Daniel S. Lo. 2014. Finite element mesh generation. CRC Press.
90. Jianhua Lu, Haifeng Han, Baochang Shi, and Zhaoli Guo. 2012. Immersed boundary lattice Boltzmann model based on multiple relaxation times. Physical Review E 85, 1 (2012), 016711.
91. Chaoyang Lyu, Wei Li, Mathieu Desbrun, and Xiaopei Liu. 2021. Fast and Versatile Fluid-Solid Coupling for Turbulent Flow Simulation. ACM Trans. Graph. 40, 6, Article 201 (2021).
92. E. Lévêque, F. Toschi, L. Shao, and J.-P. Bertoglio. 2007. Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows. Journal of Fluid Mechanics 570 (2007), 491–502.
93. Miles Macklin and Matthias Müller. 2013. Position Based Fluids. ACM Trans. Graph. 32, 4, Article 104 (2013).
94. Orestis Malaspinas. 2015. Increasing Stability and Accuracy of the Lattice Boltzmann Scheme: recursivity and regularization. arXiv:1505.06900 [physics.flu-dyn].
95. Orestis Malaspinas and Pierre Sagaut. 2011. Advanced large-eddy simulation for lattice Boltzmann methods: The approximate deconvolution model. Physics of Fluids 23, 10 (2011), 105103.
96. O. Malaspinas and P. Sagaut. 2014. Wall model for large-eddy simulation based on the lattice Boltzmann method. J. Comput. Phys. 275 (2014), 25–40.
97. Francesco Marson. 2022. Directional Lattice Boltzmann Boundary Conditions. Ph. D. Dissertation. University of Geneva.
98. Francesco Marson, Yann Thorimbert, Bastien Chopard, Irina Ginzburg, and Jonas Lätt. 2021. Enhanced Single-node Lattice Boltzmann Boundary Condition for Fluid Flows. Phys. Rev. E 103 (2021), 053308. Issue 5.
99. Keijo K. Mattila, Paulo C. Philippi, and Luiz A. Hegele. 2017. High-order Regularization in Lattice-Boltzmann Equations. Physics of Fluids 29, 4 (2017), 046103.
100. Maxon. 2023. Redshift renderer. (2023). https://www.redshift3d.com/product
101. Renwei Mei, Dazhi Yu, Wei Shyy, and Li-Shi Luo. 2002. Force evaluation in the lattice Boltzmann method involving curved geometry. Phys. Rev. E 65 (2002), 041203. Issue 4.
102. Florian R. Menter. 1994. Two-equation Eddy-viscosity Turbulence Models for Engineering Applications. AIAA Journal 32, 8 (1994), 1598–1605.
103. Markus Mohrhard, Gudrun Thäter, Jakob Bludau, Bastian Horvat, and Mathias J. Krause. 2019. Auto-vectorization friendly parallel lattice Boltzmann streaming scheme for direct addressing. Computers & Fluids 181 (2019), 1–7.
104. Faith A. Morrison. 2013. An introduction to fluid mechanics. Cambridge University Press.
105. Matthias Müller, David Charypar, and Markus Gross. 2003. Particle-Based Fluid Simulation for Interactive Applications. In Symposium on Computer Animation. 154–159.
106. Patrick Nathen, Marc Haussmann, Mathias J. Krause, and Nikolaus A. Adams. 2018. Adaptive filtering for the simulation of turbulent flows with lattice Boltzmann methods. Computers & Fluids 172 (2018), 510–523.
107. X. B. Nie, X. Shan, and H. Chen. 2008. Galilean invariance of lattice Boltzmann models. Europhysics Letters 81, 3 (2008), 34005.
108. Sang Il Park and Myoung Jun Kim. 2005. Vortex Fluid for Gaseous Phenomena. In Symposium on Computer Animation. 261–270.
109. Jitendra Kumar Patel and Ganesh Natarajan. 2018. Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies. J. Comp. Phys. 360 (2018), 202–228.
110. Charles S. Peskin. 1972. Flow patterns around heart valves: a numerical method. J. Comp. Phys. 10, 2 (1972), 252–271.
111. Tobias Pfaff, Nils Thuerey, and Markus Gross. 2012. Lagrangian Vortex Sheets for Animating Fluids. ACM Trans. Graph. 31, 4, Article 112 (2012), 8 pages.
112. Kannan N. Premnath, Martin J. Pattison, and Sanjoy Banerjee. 2009. Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method. Physica A: Statistical Mechanics and its Applications 388, 13 (2009), 2640–2658.
113. Ziyin Qu, Minchen Li, Fernando De Goes, and Chenfanfu Jiang. 2022. The Power Particle-in-Cell Method. ACM Trans. Graph. 41, 4, Article 118 (2022), 13 pages.
114. Ziyin Qu, Xinxin Zhang, Ming Gao, Chenfanfu Jiang, and Baoquan Chen. 2019. Efficient and Conservative Fluids Using Bidirectional Mapping. ACM Trans. Graph. 38, 4, Article 128 (2019).
115. Martin Rohde, Drona Kandhai, Jos J. Derksen, and Harry E. A. van den Akker. 2006. A Generic, Mass Conservative Local Grid Refinement Technique for Lattice-Boltzmann Schemes. International Journal for Numerical Methods in Fluids 51, 4 (2006), 439–468.
116. Gianluca Romani, Edoardo Grande, Francesco Avallone, Daniele Ragni, and Damiano Casalino. 2022. Performance and noise prediction of low-Reynolds number propellers using the Lattice-Boltzmann method. Aerospace Science and Technology 125 (2022), 107086.
117. Pierre Sagaut. 2010. Toward Advanced Subgrid Models for Lattice-Boltzmann-based Large-eddy Smulation: theoretical formulations. Computers & Mathematics with Applications 59, 7 (2010), 2194–2199.
118. Florian Schornbaum and Ulrich Rüde. 2016. Massively Parallel Algorithms for the Lattice Boltzmann Method on NonUniform Grids. SIAM J. Sci. Comput. 38, 2 (2016), C96–C126.
119. Florian Schornbaum and Ulrich Rüde. 2018. Extreme-Scale Block-Structured Adaptive Mesh Refinement. SIAM Journal on Scientific Computing 40, 3 (2018), C358–C387.
120. Andrew Selle, Ronald Fedkiw, Byungmoon Kim, Yingjie Liu, and Jarek Rossignac. 2008. An unconditionally stable MacCormack method. Journal of Scientific Computing 35, 2 (2008), 350–371.
121. Andrew Selle, Nick Rasmussen, and Ronald Fedkiw. 2005. A Vortex Particle Method for Smoke, Water and Explosions. In Proceedings of ACM SIGGRAPH. 910–914.
122. Jung Hee Seo and Rajat Mittal. 2011. A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J. Comp. Phys. 230, 19 (2011), 7347–7363.
123. Xiaowen Shan. 2019. Central-moment-based Galilean-invariant Multiple-relaxation-time Collision Model. Phys. Rev. E 100 (2019), 043308. Issue 4.
124. Xiaowen Shan and Hudong Chen. 2007. A General Multiple-relaxation-time Boltzmann Collision Model. International Journal of Modern Physics C 18, 4 (2007), 635–643.
125. Ratnesh K Shukla, Mahidhar Tatineni, and Xiaolin Zhong. 2007. Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations. J. Comput. Phys. 224, 2 (2007), 1064–1094.
126. Siemens PLM Software. 2023. Simcenter STAR-CCM+ 2210. Siemens.
127. Dassault Systèmes Simulia Corp. 2023. 3DEXPERIENCE SIMULIA. Dassault Systèmes.
128. Giovanni Solari. 2019. Wind Science and Engineering: Origins, Developments, Fundamentals and Advancements. Springer.
129. B. Solenthaler and R. Pajarola. 2009. Predictive-Corrective Incompressible SPH. In Proceedings of ACM SIGGRAPH. Article 40, 6 pages.
130. Jos Stam. 1999. Stable Fluids. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. 121–128.
131. John C. Strikwerda. 2004. Finite Difference Schemes and Partial Differential Equations, Second Edition. SIAM.
132. Xiangshuo Tang, Yue Yu, and Alparslan Oztekin. 2022. Asymptotic Method for Entropic Multiple Relaxation Time Model in Lattice Boltzmann Method. Phys. Rev. E 106 (2022), 015303. Issue 1.
133. Shi Tao, Qing He, Baiman Chen, Xiaoping Yang, and Simin Huang. 2018. One-point Second-order Curved Boundary Condition for Lattice Boltzmann Simulation of Suspended Particles. Computers & Mathematics with Applications 76, 7 (2018), 1593–1607.
134. Shi Tao, Junjie Hu, and Zhaoli Guo. 2016. An investigation on momentum exchange methods and refilling algorithms for lattice Boltzmann simulation of particulate flows. Computers & Fluids 133 (2016), 1–14.
135. Shashank S. Tiwari, Eshita Pal, Shivkumar Bale, Nitin Minocha, Ashwin W. Patwardhan, Krishnaswamy Nandakumar, and Jyeshtharaj B. Joshi. 2020. Flow past a single stationary sphere, 2. Regime mapping and effect of external disturbances. Powder Technology 365 (2020), 215–243.
136. Jiyuan Tu, Guan Heng Yeoh, and Chaoqun Liu. 2018. Computational fluid dynamics: a practical approach. Butterworth-Heinemann.
137. Milton Van Dyke. 1982. An album of fluid motion. The Parabolic Press.
138. Mathias Weickert, Gerd Teike, Oliver Schmidt, and Martin Sommerfeld. 2010. Investigation of the LES WALE turbulence model within the lattice Boltzmann framework. Computers & Mathematics with Applications 59, 7 (2010), 2200–2214.
139. Steffen Weißmann and Ulrich Pinkall. 2010. Filament-Based Smoke with Vortex Shedding and Variational Reconnection. In Proceedings of ACM SIGGRAPH. Article 115.
140. Kui Wu, Nghia Truong, Cem Yuksel, and Rama Hoetzlein. 2018. Fast Fluid Simulations with Sparse Volumes on the GPU. Computer Graphics Forum 37, 2 (2018), 157–167.
141. Dazhi Yu, Renwei Mei, and Wei Shyy. 2003. A Unified Boundary Treatment in Lattice Boltzmann Method. In Aerospace Sciences Meeting and Exhibit. 953.
142. Jonas Zehnder, Rahul Narain, and Bernhard Thomaszewski. 2018. An Advection-Reflection Solver for Detail-Preserving Fluid Simulation. ACM Trans. Graph. 37, 4, Article 85 (2018), 8 pages.
143. Raoyang Zhang, Xiaowen Shan, and Hudong Chen. 2006. Efficient Kinetic Method for Fluid Simulation beyond the Navier-Stokes Equation. Phys. Rev. E 74 (2006), 046703. Issue 4.
144. Xinxin Zhang and Robert Bridson. 2014. A PPPM Fast Summation Method for Fluids and Beyond. ACM Trans. Graph. 33, 6, Article 206 (2014).
145. Xinxin Zhang, Robert Bridson, and Chen Greif. 2015. Restoring the Missing Vorticity in Advection-Projection Fluid Solvers. ACM Trans. Graph. 34, 4, Article 52 (2015).
146. Zheyan Zhang, Yongxing Wang, Peter K Jimack, and He Wang. 2020. MeshingNet: A new mesh generation method based on deep learning. In International Conference on Computational Science. Springer, 186–198.
147. Weifeng Zhao, Juntao Huang, and Wen-An Yong. 2019. Boundary Conditions for Kinetic Theory Based Models I: lattice Boltzmann models. Multiscale Modeling & Simulation 17, 2 (2019), 854–872.
148. Weifeng Zhao and Wen-An Yong. 2017. Single-node Second-order Boundary Schemes for the Lattice Boltzmann Method. J. Comp. Phys. 329 (2017), 1–15.
149. Yongning Zhu and Robert Bridson. 2005. Animating Sand as a Fluid. ACM Trans. Graph. 24, 3 (2005), 965–972.
150. Olgierd C. Zienkiewicz, Robert L. Taylor, and J.Z. Zhu. 2013. The Finite Element Method: its Basis and Fundamentals. Butterworth-Heinemann.
