Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

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Simulating Liquid Sound Will Moss Hengchin Yeh
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Transcript of Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Page 1: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Simulating Liquid SoundWill Moss

Hengchin Yeh

Page 2: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Part I: Fluid Simulation forSound Rendering

Page 3: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Solve the Navier-Stokes equations

where v is the flow velocity, ρ is the fluid density, p is the pressure, T is the (deviatoric) stress tensor, and f represents body forces

Liquid Simulation

Page 4: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Generally, graphics people assume the fluid is incompressible and inviscid (no viscosity)

Looks fine for water and other liquids.

Cannot handle shockwaves or acoustic wavesFor these, wee work by Jason or Nikunj

Liquid Simulation

Page 5: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Sound GenerationMore detail in the second half

Sound is generated by bubblesOur fluid simulator must be able to handle

bubbles

Page 6: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Fluid Simulation TechniquesGrid Based (Eulerian)

Accurate to within the grid resolutionSlow

Particle Based (Lagrangian)FasterCan look a little strange

OthersShallow water equationsCoupled shallow water and particle based

Page 7: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Grid Based MethodsSplit the inviscid, incompressible Navier-Stokes

equations into the three partsAdvectionForcePressure

Correct within a factor of O(Δt)

Page 8: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Grid Based MethodsConsiders a constant grid and observes what

moves into an out of a cellStagger the grid points to avoid problems

Measure the pressure at the center of a grid cell Measure the velocity at the faces between the grid

points

u

x

Page 9: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Grid Based Methods

ui 12, j ui 12, jvi, j 12

pi, j pi1, j

pi, j 1

pi, j1

pi 1, j

vi, j 12

Page 10: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Grid Based MethodsNaturally handle bubbles

Just grid cells that are empty with liquid surrounding them Must take rendering into account

Used in boiling simulations (Kim, et al)Demos

Early Foster and FedkiwFluid-fluid interactionsBoiling

Page 11: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Particle Based MethodsParticles are created by an emitter and exist

for a certain length of timeStore mass, position, velocity, external forces

and their lifetimeNo particle interactionsBased on smoothed particle hydrodynamics

[CITE]

Page 12: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Particle InteractionsNo particle interactions

Fast, system is decoupledCan only simulate splashing and

sprayingParticle Interactions

Theoretically n2 interactions Define a cutoff distance outside of

which particles do not interactAllows for puddles, pools, etc.

Page 13: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Particle InteractionsInteractions of liquids look

something like

Mathematically we model this with:

Page 14: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Smoothed Particle HydrodynamicsNavier-Stokes equations operate on continuous fields, but

we have particlesAssume each particle induces a smooth local fieldThe global fluid field is simply the sum of all the local fields

Page 15: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Equations of MotionSimple particle equations:

Reformulate Navier-Stokes equations in terms of forcesEach particle feels a force due to pressure, viscosi

ty and any external forces

Page 16: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

BubblesBubbles are not inherently handled (like in Eule

rian approaches)Add an air particle to the system

Create air particles at the surface, so they can be incorporated into the fluid

Add a interaction force and a surface tension force to the particles

Page 17: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Smoothed Particle HydrodynamicsDemos

Simple SPH DemoAdding air particles

Boiling Pouring

Page 18: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Shallow Water EquationsReduce the problem to 2D

At each x and y in the grid, store the height of the fluidDrastically reduces the complexity of the Navier-Stokes equ

ations Runs in real time

Page 19: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Shallow Water EquationsOne value for each grid cell means no bubbles o

r breaking wavesExtension to the method by Thuerey, et. Al

Simulate the bubbles as particles interacting with the fluid

Can also simulate foam on the surface with SPH particles

Video

Page 20: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Small Bubbles?What about small scale bubbles?

Increase the resolution Computationally expensive

Use finer grid sizes near the surface Complicated, still expensive

Use a heuristic near the surface Inaccurate, but faster We have seen before, sounds can be inaccurate and

still portray the necessary feeling

Page 21: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

HeuristicsAssume bubbles and foam form at regions of th

e surface where measureable quantities exceed a thresholdCould use curvature, divergence, Jacobian, etc.Generate bubble profiles for those regions heurist

ically based on the physical propertiesOther heuristics possible

Page 22: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Texture SynthesisUsed at UNC for generating realistic textures

for dynamic fluidsVideo

Page 23: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

References Thürey, N., Sadlo, F., Schirm, S., Müller-Fischer, M., and Gross, M. 2007.

“Real-time simulations of bubbles and foam within a shallow water framework”. In Proceedings of the 2007 ACM Siggraph/Eurographics Symposium on Computer Animation

Müller, M., Solenthaler, B., Keiser, R., and Gross, M. 2005. “Particle-based fluid-fluid interaction”. In Proceedings of the 2005 ACM Siggraph/Eurographics Symposium on Computer Animation

Bridson, R. and Müller-Fischer, M. 2007. Fluid simulation: SIGGRAPH 2007 course notes

Narain, R., Kwatra, V., Lee, H.P., Kim, T., Carlson, M., and Lin, M.C., Feature-Guided Dynamic Texture Synthesis on Continuous Flows, Eurographics Symposium on Rendering 2007.

Foster, N. and Fedkiw, R. 2001. Practical animation of liquids. In Proceedings of the 28th Annual Conference on Computer Graphics and interactive Techniques SIGGRAPH '01

Page 24: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Part II: Bubble Sound

Page 25: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Cavitation InceptionTensile Strength Cavitation Nuclei

InsideVacuumGasVapor

Spherical Bubble

pi=pg+pv

ps

pL

R

p0

Hydrostatic pressure

Page 26: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Free Oscillation

=0

ps + pL > pi

pi

=0

Rmax

Rmin

R0

R0

pi

ContractingStart from wall speed =0 ps + pL > piInternal pressure builds up as ai

r is compressedadiabatically (PV = const. ) isothermally (PV=nRT)

Expandingwall speed =0ps + pL < piInternal pressure decreases

Page 27: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Rayleigh-Plesset EquationR-P eq.

Work done by pressure difference =Kinetic Energy (Speed of wall)+ Viscosity damping μ+ (Acoustic radiation)+ (Thermal damping)

Page 28: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Linearization of R-P eq.R-P eq. is non-linearLinearization for R = R0+r

Solution without damping

Minnaert Resonance Frequence

Page 29: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

DampingDamped Solution

Shifted resonance freq.

Damping factor

Page 30: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

DampingRadiation

Viscosity

Thermal

Page 31: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Shifted Resonant Frequency

Large Bubble Assumption R > 0.1 mm, safely use Minnaert Fr

eq. 20hz ~ 20000hz 0.15m ~ 0.15mm

Page 32: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Pressure RadiationRelate R to pressure

Assume a Newtonian fluid of constant density

sound speed cwall speed amplitude U0

Result

is the acoustic pressure radiated by the source at unit distance from that source

Page 33: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Experiments

Page 34: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

Nonspherical Bubble OscillationsSpherical Harmonics

Related to Oscillation modes

Page 35: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

BurstBefore burst

ThinningInstabilityInterference

magnifiedMove around

very fast.

Burst when wall is still much thicker than 10 nm, the barrier

Page 36: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

More IssueObstructionChange in Speed of SoundCouplingPopping excitation.

Page 37: Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.

References [1] J. Ding et al., “Acoustical observation of bubble oscillations induced by bubble p

opping,” Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), vol. 75, Apr. 2007, pp. 041601-7.

[2] A. M S Plesset and A Prosperetti, “Bubble Dynamics and Cavitation,” Nov. 2003; http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.fl.09.010177.001045.

[3] D. Lohse, “Bubble Puzzles,” Physics Today, vol. 56, 2003, pp. 36-41. [4] S. Nagrath et al., “Hydrodynamic simulation of air bubble implosion using a lev

el set approach,” Journal of Computational Physics, vol. 215, Jun. 2006, pp. 98-132. [5] T.B. Benjamin, “Note on shape oscillations of bubbles,” Journal of Fluid Mecha

nics Digital Archive, vol. 203, 2006, pp. 419-424. [6] R. Manasseh et al., “Passive acoustic bubble sizing in sparged systems,” Experi

ments in Fluids, vol. 30, Jun. 2001, pp. 672-682. [7] K. Lunde and R.J. Perkins, “Shape Oscillations of Rising Bubbles,” Applied Scie

ntific Research, vol. 58, Mar. 1997, pp. 387-408. [8]“Sound emission on bubble coalescence: imaging, acoustic and numerical exper

im”; http://espace.library.uq.edu.au/view/UQ:120769. [9] T.G. Leighton, The acoustic bubble, London: Academic Press, 1994. [10] H.C. Pumphrey and P.A. Elmore, “The entrainment of bubbles by drop impacts

,” Journal of Fluid Mechanics Digital Archive, vol. 220, 2006, pp. 539-567.