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FLUID MODELING with STOCHASTIC and STRUCTURAL FEATURES a Dissertation Submitted to Kent State University in Partial Fulfillment

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FLUID MODELING with STOCHASTIC and STRUCTURAL FEATURES a Dissertation Submitted to Kent State University in Partial Fulfillment FLUID MODELING WITH STOCHASTIC AND STRUCTURAL FEATURES A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Zhi Yuan August 2013 Dissertation written by Zhi Yuan B.S., Huazhong University of Science and Technology, 2005 Ph.D., Kent State University, 2013 Approved by Dr. Ye Zhao , Chair, Doctoral Dissertation Committee Dr. Ruoming Jin , Members, Doctoral Dissertation Committee Dr. Austin Melton Dr. Xiaoyu Zheng Dr. Robin Selinger Accepted by Dr. Javed Khan , Chair, Department of Computer Science Dr. Raymond A. Craig , Dean, College of Arts and Sciences ii TABLE OF CONTENTS LISTOFFIGURES..................................... vi LISTOFTABLES ..................................... ix Acknowledgements ................................... .. x Dedication......................................... xi 1 Introduction ...................................... 1 1.1 Significance,ChallengeandObjectives. ........ 1 1.2 MethodologyandContribution . .... 3 1.3 Background.................................... 5 1.3.1 PhysicallyBasedFluidSimulationMethods . ...... 5 1.3.2 FluidTurbulence ............................. 6 1.3.3 FluidControl ............................... 7 1.3.4 FluidCompression ............................ 8 2 Incorporating Fluctuation and Uncertainty in Particle-basedFluidSimulation. 10 2.1 Introduction.................................... 10 2.2 BasicSPHAlgorithm............................... 15 2.3 StochasticTurbulenceinSPH . ... 16 2.4 TurbulenceEvolution . .. 17 iii 2.4.1 Production ................................ 17 2.4.2 Development ............................... 19 2.4.3 Spreading................................. 19 2.5 Discussion..................................... 20 2.6 Results....................................... 21 3 Stochastic Modeling of Light-weight Floating Objects . .............. 30 3.1 Introduction.................................... 30 3.2 k ε TurbulenceModel ............................. 33 − 3.3 StochasticObjectMotion. ... 35 3.4 ImplementationandResults . ... 37 4 Pattern-based Smoke Animation with Lagrangian Coherent Structure . 40 4.1 Introduction.................................... 40 4.2 FlowPattern.................................... 44 4.2.1 Finite-TimeLyapunovExponent(FTLE) . ... 46 4.2.2 ForwardandBackwardFTLE . 47 4.2.3 LagrangianCoherentStructure(LCS) . .... 48 4.2.4 Thinning ................................. 50 4.2.5 Implementation.............................. 51 4.3 Pattern-drivenFluidAnimation. ...... 52 4.4 ResultsandPerformance . .. 53 5 Ad Hoc CompressionofSmokeAnimation. 61 iv 5.1 Introduction.................................... 61 5.2 CompressionFramework . 64 5.3 Inter-frame Compression with Bidirectional Advection ............. 66 5.3.1 AdaptiveVelocitySimplificationwithFTLE . ..... 68 5.3.2 ReconstructionfromMotionVectors. .... 70 5.3.3 BidirectionalAdvectionandWeightMap . .... 71 5.4 Intra-frameCompression . ... 74 5.5 Decompression .................................. 77 5.6 ExperimentsandPerformance . ... 77 5.7 Discussion..................................... 85 6 FutureWork....................................... 87 6.1 Improving Turbulence Enhancement and Fluid Control . .......... 87 6.2 TexturebasedFluidAppearanceEnhancement . ........ 88 6.2.1 AdvectedTexturebasedonFlowPatterns . .... 88 6.2.2 Optimization based Texture Synthesis using Flow Patterns ....... 90 6.3 TrajectoryAnalysisandVisualization . ........ 91 7 Conclusion........................................ 94 BIBLIOGRAPHY...................................... 95 v LIST OF FIGURES 1 Snapshotsof2Dturbulenceevolution. ..... 21 2 Snapshots of 2D turbulence induced by object. (a) Use object introduced SIPs without turbulence spreading; (b) With medium turbulence spreading; (c) With strong turbulence spreading; (d) Use a large number of initial SIPs without turbulencespreading. .. .. .. .. .. .. .. .. 22 3 Snapshots of a moving object inside a water tank along different time steps (a)-(d). Top: Original SPH simulation; Bottom: With introduced turbulence. 25 4 Snapshots of a moving object inside a water tank in comparison with using vortexparticles................................... 26 5 Snapshots of a water stream with obstacle-induced SIPs. (a) Original placid simulation; (b)-(c) With introduced turbulence at differentsteps. 27 6 Snapshots of water pouring into a tank. (a) Original simulation with smooth surface; (b)-(c) With added fluctuation at different steps. ............ 28 7 Snapshotsofwaterpouringintoalargertank. ....... 29 8 Diagramofouralgorithm. ............................ 32 9 Simulation snapshots of flying leaves past a house based on a pre-computed stationaryvelocityfield.. .. 38 10 Overviewofourmethod. ............................. 43 vi 11 Flow pattern with FTLE and LCS. (a) Red: upward velocity. Green: downward velocity; (b)(c) Red: high FTLE value; Blue: low FTLE value; (d)(e) LCS regionfrom(c). .................................. 45 12 ControldomainwithLCSthinningfromFig. 11(e). ........ 48 13 2D Pattern-based fluid animation. (a) Low-resolution simulation result; (b) High-resolution simulation with regulation after 10 thinning passes; (c) High- resolution simulation with regulation after 20 thinning passes; (d) High-resolution simulationwithoutregulation. ... 49 14 Pattern-based fluid animation on a moving ball simulation. (a) Low-resolution simulation result; (b) High-resolution simulation with regulation; (c) High- resolution simulation with regulation after 8 passes of thinning; (d) High- resolutionsimulationwithoutregulation. ........ 57 15 Pattern visualization of the Fig. 23 example. (a) 4 thinnings; (b) 8 thinnings; (c)12thinnings................................... 58 16 Pattern-based fluid animation on vortex particles. (a) Low-resolution simu- lation result; (b) Adding vortex particles with regulation (4 thinnings); (c) Addingvortexparticleswithoutregulation. ....... 59 17 Pattern-based fluid animation on turbulence enhancement with wavelet noise. (a) Low-resolution simulation result; (b) Adding noise with regulation (8 thin- nings);(c)Addingnoisewithoutregulation. ....... 60 18 Smokeanimationframeworkoverview. .... 64 vii 19 Illustration of the adaptive velocity simplification with FTLE. The domain is divided into nonuniform blocks based on FTLE. (a) 2D velocity field (256 × 256); (b) FTLE field; (c) Motionvectors overthe blockswith the smallest block at 8 8 and the largest block at 64 64...................... 67 × × 20 Bidirectional advection for P-Frames estimation from two consecutive K-Frames. Red and purple arrow lines represent forward advection and backward advec- tion,respectively. ................................. 71 21 Using different CP , the number of P-Frames between two K-Frames, in com- pression. (a) One K-Frame with CP =5; (b) CP = 20 compared with (a); (c) One middle P-Frame with CP =5; (d) CP = 20 comparedwith(c). 75 22 Snapshots of smoke animation created from decompressed density volumes (192 256 192) after compression. (a) Original data with no compression × × (clip size: 1.4GB); (b) Compression by our method (compressed clip size: 7.1MB); (c) Visualize the difference of (b) from (a) in red; (d) Compression by extending 2D video compression techniques to 3D volumes (compressed clip size: 8.4MB); (e) Visualize the difference of (d) from (a) in red. Here, (b)(c) and (d)(e) achieve a similar compression ratio around 200 compared to (a), but (d)(e) introduce excessive aliasing which is destructiveinthevideo. 78 23 Usingdifferent C in compression with a 250 320 250 simulation. 79 P × × 24 Varied compression cases. (a) Using DCT quantization coefficient φ = 0.4; (b) Using a smaller rendering scattering coefficient σs ............. 83 25 FlowPatternsforAnimalTrajectory. ...... 93 viii LIST OF TABLES 1 Experimentsparameters. ............................ 24 2 PerformanceReport(inseconds).. .... 55 3 Compression performance of several smoke animation clips. The clips are created in a short time period from different smoke simulations. The weight map quantization coefficient ω = 5 and the DCT quantization coefficient φ = 0.01......................................... 76 4 QualityMeasurementofTable3. .. 81 5 Using different weight map quantization coefficient ω. ............. 82 6 Using different DCT quantization coefficient φ.................. 84 7 Computing performance per step in milliseconds. MV: motion vector gener- ation; u∗: reconstruction of velocities from motion vector; ω: weight map generation; Inv. DCT: inverse DCT transform. ..... 85 ix Acknowledgements First and foremost, I want to express my deepest gratitude to my advisor, Professor Ye Zhao, who leads me into the colorful world of computer graphics with his persistent vision, patience and encouragement. Thanks a lot, Dr. Special thanks to my committee, Dr. Ruoming Jin, Dr. Austin Melton, Dr. Xiaoyu Zheng and Dr. Robin Selinger. Their support and guidance are highly beneficial to me. I also want to thanks Dr. Cheng Chang Lu for the advice and discussion of some work in this thesis, and Dr. Paul A. Farrell for the support during my candidacy exam. To all the friends in Graphics and Visualization Lab, I enjoyed every moment with you guys. Most of my work is supported by U.S. National Science Foundation under grant IIS-0916131. x To my lovely family xi CHAPTER 1 Introduction 1.1 Significance, Challenge and Objectives Physically-based fluid simulation has achieved great success in computer graphics with a vari- ety of astounding appearances of splashing water, burning
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