Abstract
The scope of this work involves the integration of high-speed parallel computation with interactive, 3D visualization of the lattice-Boltzmann-based immersed boundary method for fluid–structure interaction. An NVIDIA Tesla K40c is used for the computations, while an NVIDIA Quadro K5000 is used for 3D vector field visualization. The simulation can be paused at any time step so that the vector field can be explored. The density and placement of streamlines and glyphs are adjustable by the user, while panning and zooming is controlled by the mouse. The simulation can then be resumed. Unlike most scientific applications in computational fluid dynamics where visualization is performed after the computations, our software allows for real-time visualizations of the flow fields while the computations take place. To the best of our knowledge, such a tool on GPUs for FSI does not exist. Our software can facilitate debugging, enable observation of detailed local fields of flow and deformation while computing, and expedite identification of ‘correct’ parameter combinations in parametric studies for new phenomenon. Therefore, our software is expected to shorten the ‘time to solution’ process and expedite the scientific discoveries via scientific computing.
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Lenovo D30, 8 core E5-2609@2.4GHz, 32GB RAM, Windows 7/64.
References
Tian FB, Luo H, Zhu L, Lu XY (2010) Interaction between a flexible filament and a downstream rigid body. Phys Rev E 82:026301
Espinha LC, Hoey DA, Fernandes PR, Rodrigues HC, Jacobs CR (2014) Oscillatory fluid flow influences primary cilia and microtubule mechanics. Cytoskeleton 71:435–445
Huang S, Li R, Li QS (2013) Numerical simulation on fluid–structure interaction of wind around super-tall building at high reynolds number conditions. Struct Eng Mech Int J 46:197–212
Peskin CS (2002) The immersed boundary method. Acta Numer 11:409
Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37:239–261
LeVeque RJ, Li ZL (1997) Immersed interface methods for Stokes flows with elastic boundaries or surface tension. SIAM J Sci Comput 18:709–735
Cortez R (2000) A vortex/impulse method for immersed boundary motion in high Reynolds number flows. J Comput Phys 160:385–400
Wang XS (2006) From immersed boundary method to immersed continuum method. Int J Multiscale Comput Eng 4:127–145
Zhang L, Gersternberger A, Wang X, Liu WK (2004) Immersed finite element method. Comput Methods Appl Mech Eng 193:2051
Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349
Glowinski R, Pan T, Periaux J (1994) A fictitious domain method for Dirichlet problem and applications. Comput Methods Appl Mech Eng 111:1994
Sulsky D, Chen Z, Schreyer HL (1994) A particle method for history-dependent materials. Comput Mech Appl Mech Eng 118:179–197
Cottet G-H, Maitre E (2006) A level set method for fluid–structure interactions with immersed surfaces. Math Models Methods Appl Sci 16:415–438
Kim J-D, Li Y, Li X (2013) Simulation of parachute FSI using the front tracking method. J Fluids Struct 37:100–119
Peskin CS (1972) Flow patterns around heart valves: a digital computer method for solving the equations of motion, vol 378. PhD thesis. Physiology, Albert Einstein College of Medicine, University of Microfilms, pp 72–30
Peskin CS (1977) Flow patterns around heart valves; a numerical method. J Comput Phys 25:220
McCracken MF, Peskin CS (1980) A vortex method for blood flow through heart valves. J Comput Phys 35:183–205
Rosar ME, Peskin CS (2001) Fluid flow in collapsible elastic tubes: a three-dimensional numerical model. New York J Math 7:281–302
Roma AM, Peskin CS, Berger MJ (1999) An adaptive version of the immersed boundary method. J Comput Phys 153:509–534
Lai MC, Peskin CS (2000) An immersed boundary method with formal second order accuracy and reduced numerical viscosity. J Comput Phys 160:705
Griffith BE, Peskin CS (2015) On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficient smooth problems. J Comput Phys 208:75–105
Zhu L, Peskin CS (2002) Simulation of a flexible flapping filament in a flowing soap film by the immersed boundary method. J Comput Phys 179:452–468
Kim Y, Peskin CS (2007) Penalty immersed boundary method for an elastic boundary with mass. Phys Fluids 19:053103
Fauci LJ, Fogelson AL (1993) Truncated Newton methods and the modeling of complex elastic structures. Commun Pure Appl Math 46:787
Taira K, Colonius T (2007) The immersed boundary method: a projection approach. J Comput Phys 225:2118–2137
Mori Y, Peskin CS (2008) Implicit second-order immersed boundary method with boundary mass. Comput Methods Appl Mech Eng 197:2049–2067
Hao J, Zhu L (2010) A lattice Boltzmann based implicit immersed boundary method for fluid–structure-interaction. Comput Math Appl 59:185–193
Hao J, Zhu L (2011) A 3D implicit immersed boundary method with application. Theor Appl Mech Lett 1:062002
Lim S, Ferent A, Wang XS, Peskin CS (2008) Dynamics of a closed rod with twist and bend in fluid. SIAM J Sci Comput 31:273–302
Atzberger PJ, Kramer PR, Peskin CS (2006) A stochastic immersed boundary method for biological fluid dynamics at microscopic length scale. J Comput Phys 224:1255–1292
Zhu L, He G, Wang S, Miller L, Zhang X, You Q, Fang S (2011) An immersed boundary method based on the lattice Boltzmann approach in three dimensions with application. Comput Math Appl 61:3506–3518
Feng ZG, Michaelides EE (2005) Proteus: a direct forcing method in the simulations of particulate flows. J Comput Phys 202:20–51
Tian FB, Luo H, Zhu L, Liao JC, Lu X-T (2011) An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J Comput Phys 230(19):7266–7283
Zhang C, Cheng Y, Zhu L, Wu J (2016) Accuracy improvement of the immersed boundary-lattice Boltzmann coupling scheme by iterative force correction. Comput Fluids 124:246–260
Wu J, Shu C (2009) Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications. J Comput Phys 228:1963–1979
Niu XD, Shu C, Chew YT, Peng Y (2006) A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows. Phys Lett A 354:173–182
Wu J, Shu C, Zhang YH (2010) Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary-lattice Boltzmann method. Int J Numer Methods Heat Fluid Flow 62:327–354
Cheng Y, Zhu L, Zhang C (2014) Numerical study of stability and accuracy of the immersed boundary method coupled to the lattice Boltzmann BGK model. Commun Comput Phys 16:136–168
Cheng Y, Zhang H (2010) Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow. Comput Fluids 39:871–881
Shu C, Liu N, Chew Y-T (2007) A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder. J Comput Phys 226:1607–1622
Liu N, Peng Y, Liang Y, Lu X (2012) Flow over a traveling wavy foil with a passively flapping flat plate. Phys Rev E 85:056316
Lee P, Griffith BE, Peskin CS (2010) The immersed boundary method for advection–electrodiffusion with implicit timestepping and local mesh refinement. J Comput Phys 229:5208–5227
Fai TG, Griffith BE, Mori Y, Peskin CS (2014) Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers II: theory. SIAM J Sci Comput 36:B589–B621
Huang H, Sukop M, Lu X (2015) Multiphase lattice Boltzmann methods: theory and application. Wiley, Hoboken
Guo Z, Shu C (2013) Lattice Boltzmann method and its applications in engineering. World Scientific, Singapore
Qian YH (1990) Lattice gas and lattice kinetic theory applied to the Navier-Stokes equations, PhD thesis. University Pierre et Marie Curie, Paris (1990)
Hou S, Zou Q, Chen S, Doolen G, Cogley A (1995) Simulation of cavity flow by the lattice Boltzmann method. J Comput Phys 118:329
He X, Chen S, Zhang R (1999) A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. J Comput Phys 152:642–663
Wolf-Gladrow DA (2000) Lattice-gas cellular automata and lattice Boltzmann models—an introduction. Springer, Berlin
Succi S (2001) The lattice Boltzmann equation. Oxford Univ Press, Oxford
Luo LS (1998) Unified theory of the lattice Boltzmann models for nonideal gases. Phys Rev Lett 81:1618
Kraus J (2014) Optimizing a LBM code for compute clusters with Kepler GPUs. http://on-demand.gputechconf.com/gtc/2014/presentations/S4186-optimizing-lbm-code-compute-clusters-kepler-gpus.pdf
Valero-Lara P, Igual FD, Prieto-Matías Pinelli A, Favier J (2015) Accelerating fluid–solid simulations (lattice-Boltzmann & immersed-boundary) on heterogeneous architectures. J Comput Sci 10:249–261
Mawson M, Valero-Lara P, Favier J, Pinelli A, Revell A (2013) Fast fluid–structure interaction using lattice Boltzmann and immersed boundary methods. In: NVIDIA GPU Conference
Wu J, Cheng Y, Zhou W, Zhang C, Diao W (2016) GPU acceleration of FSI simulations by the immersed boundary-lattice Boltzmann coupling scheme. Comput Math Appl. doi:10.1016/j.camwa.2016.10.005
Bhaniramka P, Demange Y (2002) OpenGL volumizer: a toolkit for high quality volume rendering of large data sets. In: 2002 Symposium on Volume Visualization and Graphics, pp 45–53
Ahrens J, Geveci B, Law C (2005) ParaView: an end user tool for large data visualization. Visualization Handbook, Elsevier. ISBN 13:978-0123875822
Childs H, Brugger E, Whitlock B, Meredith J, Ahern S, Pugmire D, Biagas K, Miller M, Harrison C, Weber GH, Krishnan H, Fogal T, Sanderson A, Garth C, Bethel E, Camp D, Rübel O, Durant M, Favre JM, Navrátil P (2012) VisIt: an end-user tool for visualizing and analyzing very large data. In: High performance visualization—enabling extreme-scale scientific insight, pp 357–372
Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases, I; small amplitude process in charged and neutral one-component system. Phys Rev 94:511
Bailey M, Cunningham S (2012) Graphics shaders theory and practice, 2nd edn. CRC Press, Boca Raton
Weiskopf D (2006) GPU based interactive visualization techniques. Springer, Berlin
Telea AC (2015) Data visualization principles and practice, 2nd edn. CRC Press, Boca Raton
Yu H, Wang C, Ma KL (2007) Parallel hierarchical visualization of large time-varying 3D vector fields. In: Proceedings of the 2007 ACM/IEEE conference on Supercomputing, ACM, Nov 16, p 24
Xu C, Prince J (1998) Snakes, shapes, and gradient vector flow. IEEE Trans Image Process 7:359–369
Spencer B, Laramee RS, Chen G, Zhang E (2009) Evenly space streamlines for surfaces: an image based approach. Comput Graph Forum 28:1618–1631
Max N, Becker B, Crawfis R (1993) Flow volumes for interactive vector field visualization. In: Proceedings Visualization ’93, pp 19–24
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The authors would like to thank the NSF support under the Grant award Number DMS-1522554.
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Zigon, B., Zhu, L. & Song, F. Interactive 3D simulation for fluid–structure interactions using dual coupled GPUs. J Supercomput 74, 37–64 (2018). https://doi.org/10.1007/s11227-017-2103-x
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DOI: https://doi.org/10.1007/s11227-017-2103-x