ENHANCING FLUID MODELING WITH TURBULENCE AND ACCELERATION A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Fan Chen May 2015 Dissertation written by Fan Chen B.S., Huazhong University of Science and Technology, 2005 M.S., Huazhong University of Science and Technology, 2007 M.S., Kent State University, 2009 Ph.D., Kent State University, 2015 Approved by Dr. Ye Zhao , Chair, Doctoral Dissertation Committee Dr. Feodor Dragan , Members, Doctoral Dissertation Committee Dr. Arden Ruttan Dr. Jing Li Dr.Mina Katramatou Accepted by Dr. Javed Khan , Chair, Department of Computer Science Dr.James L. Blank , Dean, College of Arts and Sciences ii TABLE OF CONTENTS LISTOFFIGURES..................................... vii LISTOFTABLES ..................................... x 1 Introduction ...................................... 1 1.1 Significance,ChallengeandObjectives. ........ 1 1.2 MethodologyandContribution . .... 3 1.3 Publications.................................... 5 2 Background ....................................... 7 2.1 FluidSimulation ................................. 7 2.2 DistanceField................................... 8 2.3 FluidTurbulence ................................. 10 2.4 GPUaccelerationinFluidModeling . ..... 13 3 DistanceField..................................... 16 3.1 Introduction.................................... 16 3.2 DistanceFieldTransform. ... 19 3.2.1 Definition................................. 19 3.2.2 Vector-BasedDistanceTransform . ... 20 3.2.3 OurComputationalScheme . 21 3.3 ActiveBandScheme ............................... 22 iii 3.3.1 PropagationProcedure . 22 3.3.2 LifespanofaPoint ............................ 23 3.3.3 GridStructuresandLifespanCoefficient . ..... 25 3.4 ComputationalProcedure . ... 27 3.5 Multiple-SegmentDistanceTransform . ....... 28 3.6 ResultsandDiscussion . .. 30 4 Adaptive and Controllable Turbulence Enhancement . ............ 35 4.1 Introduction.................................... 35 4.2 RandomForcing ................................. 40 4.3 TurbulenceSynthesis . .. .. .. .. .. .. .. .. .. 41 4.3.1 FrequencyDomainGeneration. 42 4.3.2 EnergySpectrumControl . 44 4.3.3 Computation ............................... 45 4.4 TurbulenceIntegration . ... 46 4.5 ConditionalandIntermittentTurbulence . ......... 49 4.6 Experiments.................................... 53 5 LangevinParticlesinFlowSimulation . ........ 57 5.1 Introduction.................................... 57 5.2 LangevinModel.................................. 60 5.2.1 ParticleMotion:ARandomProcess . .. 60 5.2.2 GeneralizedLangevinModel. 61 5.2.3 FlowTurbulence ............................. 62 iv 5.2.4 ComputationalScheme. 63 5.3 LangevinParticlesinFlowSimulation . ....... 64 5.3.1 LangevinForce.............................. 65 5.3.2 ParticleEvolution. 66 5.3.3 TurbulenceControl............................ 68 5.3.4 SimulationProcedure. 68 5.4 Results....................................... 68 5.5 Discussion..................................... 75 6 UsingGPUinFluidModeling .. .. .. .. .. .. .. .. .. 78 6.1 GPUcomputationwithCUDA . 78 6.2 LBMSimulation ................................. 81 6.2.1 Introduction................................ 81 6.2.2 ImplementationandResults . 83 6.3 FTLE ....................................... 85 6.3.1 Introduction................................ 85 6.3.2 ImplementationandResults . 87 6.4 FluidCompression/Decompression. ...... 89 6.4.1 Compression ............................... 89 6.4.2 Decompression .............................. 90 6.4.3 Result................................... 96 7 Conclusion........................................ 98 v BIBLIOGRAPHY......................................101 vi LIST OF FIGURES 1 Floating-PointOperationsperSecond.[1] . ....... 14 2 Vectorbaseddistancepropagation. ..... 20 3 Distancetransformonarectangulargrid.. ....... 23 4 Distancetransformonatrianglegrid. ..... 26 5 The12neighborsofanFCClatticesiteformsacuboctahedron (Image courtesy ofDr.FengQiu). ................................. 26 6 DistancetransformonanFCCgrid. .. 27 7 Computational time for distance transform on different distanceranges. 32 8 Performanceofusingdifferentsegmentsize.. ........ 33 9 Distance field of the two points is rendered as isosurfaces with different dis- tancevalues..................................... 33 10 Distance field of the Armadillo is rendered as isosurfaces with different dis- tancevalues..................................... 34 11 Distance field of the bunny is rendered as isosurfaces with different distance values........................................ 34 12 Random vector fields generated for a preferred scale with different deviations. 42 13 Divergence-free vector fields with two scales. Top: Spectrum; Bottom: Vector field. µ1 = √2, µ2 =8 and σ1 = σ2 =0.7. ................... 43 14 Data flow of FNS() computation.......................... 47 vii 15 Snapshots of turbulence enhancement simulations: (a) Original coarse simu- lation; (b) Wavelet subgrid turbulence; (c) Our subgrid turbulence; (d) Add vorticity confinement to (a); (e) Wavelet turbulence to (d); (f) Our turbulence to (d) with q =0.8; (g) Our turbulence to (d) with q =0.2; (h) Our turbulence to (d) with q =0.1................................. 50 16 Snapshots of integrating turbulence to a laminar smoke. ............ 52 17 Snapshots of turbulence enhancement conditioned by the distance to obstacles: (a) a laminar smoke simulation; (b) direct turbulence integration to (a) at the same resolution; (c) Finer turbulent behavior achieved by executing simulation on a coarser grid than (a), while coupling turbulence to the interpolated flow. 55 18 Snapshots of turbulence enhancement with SPH ((b) and (d)), in comparison withoriginalsimulation((a)and(c)).. ...... 56 19 Compute Langevin force F(t). u(t) is the particle velocity, u(t) is the mean flow velocity, and u(t +1) is the particle’s target velocity at the following time step t +1 computed by Eqn. 33. ......................... 65 20 Snapshots of integrating turbulence to a rising smoke flow with two different turbulence levels controlled by the characteristic length scale lm. (a) Original flow; (b) Vorticity confinement; (c) Random forcing; (d) lm =0.001; (e) lm = 0.003. ....................................... 69 21 Snapshots of integrating turbulence to a smoke simulation with diminishing wind. Left: before wind stops; Right: after wind stops. ......... 71 22 Snapshots of turbulence enhancement of a smoke past obstacles with two dif- ferentturbulencelevels.. .. 73 viii 23 Snapshots of turbulence enhancement of a flow over a table top with two dif- ferentturbulencelevels.. .. 74 24 The GPU Devotes More Transistors to Data Processing [1]. .......... 79 25 GPUprogrammingmodel[1]. 80 26 2Dand3DLBMlattice[2]............................. 81 27 Flow pattern with FTLE and LCS. (a) Red: upward velocity. Green: downward velocity; (b)(c) Red: high FTLE value; Blue: low FTLE value. ......... 87 28 Smokeanimationframeworkoverview. .... 89 29 Bidirectional advection for P-Frames estimation from two consecutive K-Frames. Red and purple arrow lines represent forward advection and backward advec- tion,respectively. ................................. 93 30 streamcompaction[3]. ............................. 94 31 ScanAlgorithm[3]................................. 95 32 ScanandScatter[3]. ............................... 95 ix LIST OF TABLES 1 Performance of our distance transform method on multiple data sets. For each model in different grid size, we compare the computational time between seg multiple-segment method with a segment size lmax = 20 (see Section 3.5), and the method with no segment. Computational time is measured inseconds. 31 2 Performancereport................................. 75 3 SRTLBMtimecomparingbetweenCPUandGPU . 84 4 MRTLBMtimecomparingbetweenCPUandGPU . 84 5 FTLEcomputationPerformance . 88 6 Fluiddecompression ............................... 96 x CHAPTER 1 Introduction 1.1 Significance, Challenge and Objectives The applications of modeling fluid phenomena such as water, smoke, gas and fire, are widely used in computer graphics, physics, etc. A well-developed research subject called Computa- tional Fluid Dynamics(CFD) proposes many advanced numerical methods to simulate the fluid. The fundamental of CFD is Navier-Stokes equations [4] and how to efficiently and correctly solve these finite differential equations has been broadly researched and studied. In computer graphics, the fluid simulation has high expectation on reality, and the result is visually correct and not necessary to be physically correct. As the same time, the speed is also very significant in graphics applications. Therefore, how to efficiently simulate turbulent and realistic fluid has become an important objective for graphics researchers. Many researchers have endeavored to solve the Navier- Stokes equations in most two numerical methods:stable fluid solver [5] and Lattice Boltzmann Method(LBM) [6]. Stable fluid solver employed the semi-Lagrangian advection to guarantee the result unconditionally stable. This is an implicit finite-difference method to solves the NS equations. Although this method can achieve real time speed on low resolution, the accelera- tion for high resolution simulation is still needed. Because of the resource and time limitation, it is not practical to simulate the fluid at very high resolution, especially in the real-time ap- plications. On the other hand, low resolution simulation satisfies the requirement of speed