Langevin Rigid: Animating Immersed Rigid Bodies in Real-time
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1 NICOGRAPH International 2013 Session 5: Physics-based Simulation Langevin Rigid: Animating Immersed Rigid Bodies in Real-time Haoran Xie Kazunori Miyata Japan Advanced Institute of Science and Technology 1
2 Immersed Bodies All figures from Google Image 2
3 All of them cannot be animated or animated realistically by current simulation techniques in CG 3
4 Reynolds Number<>Turbulence Re<5 Steady flow 5<Re<40 Symmetric vortices 40<Re<200 Laminar vortex sheet 200<Re<200K Turbulent wake 200K<Re Fully turbulence [Journal of Fluid Mechanics 1991]
5 Coupling between Objects and Turbulence One-way coupling Newtonian Dynamics + Kutta-Joukowski theorem Swimming [SCA04, TVCG11, SIGGRAPH11] Flying [SIGGRAPH03, 09, SCA03] [Journal of Fluid Mechanics 1991] 5
![Two-way coupling Newtonian Dynamics + Navier-Stokes Equations Euler formulation and rigid bodies in Lagrangian formation[tog04, 05, 06, 07, 11,SCA06, 08,09, 10] Fully Langrangian meshless](/docs-images/96/127050710/images/6-0.jpg "method [SCA05, TVCG09, SIGGRPAH12, CGF12, SA12] Reynolds-Averaged Navier-Stokes [SA08, SIGGRPAH09,10 Eurographics12] Laminar flow Turbulent flow [Applied computational fluid dynamics,2001]")
6 Two-way coupling Newtonian Dynamics + Navier-Stokes Equations Euler formulation and rigid bodies in Lagrangian formation[tog04, 05, 06, 07, 11,SCA06, 08,09, 10] Fully Langrangian meshless method [SCA05, TVCG09, SIGGRPAH12, CGF12, SA12] Reynolds-Averaged Navier-Stokes [SA08, SIGGRPAH09,10 Eurographics12] Laminar flow Turbulent flow [Applied computational fluid dynamics,2001] 6
7 Other approaches Underwater rigid, cloth[tog2010, SIGGRAPH2012] Basset Force Kirchhoff tensor 7
8 Introduction Real-time simulation of immersed rigid bodies A Lagevin Rigid approach Coupling turbulence Inertial effect added-mass tensors Viscous effect Langevin model + Turbulence model New dynamical representation Generalized Kirchhoff equations 8
9 Overview Pre-computation Runtime 9
10 Equations of Motion World frame Kinematic Equations: 10
11 Equations of Motion Dynamic Equations: Newton s Equations Kirchhoff s Equations Generalized Kirchhoff s Equations buoyancy-corrected gravity Viscous effect Inertia effect 11
12 Equations of Motion Buoyancy-corrected gravity G B 12
13 Added-mass Tensors[SIGGRAPH2012] BD One point quadrature Potential Velocity sj where Normal flux 13
14 Turbulent model Navier-Stokes Reynolds-Averaged Navier-Stokes Turbulent viscosity Energy transport equations 14
15 Turbulent model in Implementation where Initial Conditions: 15
16 Turbulent model in Implementation Data File 16
17 Langevin Rigid Generalized Langevin Equations Wiener process where 17
18 Langevin Rigid Kirchhoff + Langevin Equations Standard Runge-Kutta Solver 18
19 Langevin Rigid 19
20 Simulation results 20
21 Simulation results Falling paper 21
22 Simulation results Flying paper-airplane 22
23 Simulation results Falling rubber ellipsoid in water [SIGGRAPH2012] Our work Ground truth 23
24 Computation costs Intel Core i7 CPU, 3.20 GHz, 12.0 GB RAM 24
25 Conclusion Real-time and realistic immersed rigid body animation Pre-computation of inertial and viscous effects Translational and rotational Langevin model Dynamic equations in Kirchhoff form 25
![Limitation and Future Work Hard to capture all characteristic motions Hybrid method with data-driven approaches [TVC 2013] Sensitive to control Toward a controllable animation Immersed](/docs-images/96/127050710/images/26-0.jpg "deformable & character animations J. Yang, F.")
26 Limitation and Future Work Hard to capture all characteristic motions Hybrid method with data-driven approaches [TVC 2013] Sensitive to control Toward a controllable animation Immersed deformable & character animations J. Yang, F., A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions, Journal of Computational Physics,
27 LANGEVIN RIGID: ANIMATING IMMERSED RIGID BODIES IN REAL-TIME Start from here~ THANK YOU! 27
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