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Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.
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Transcript of Simulating Liquid Sound Will Moss Hengchin Yeh. Part I: Fluid Simulation for Sound Rendering.
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Simulating Liquid SoundWill Moss
Hengchin Yeh
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Part I: Fluid Simulation forSound Rendering
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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
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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
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Sound GenerationMore detail in the second half
Sound is generated by bubblesOur fluid simulator must be able to handle
bubbles
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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
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Grid Based MethodsSplit the inviscid, incompressible Navier-Stokes
equations into the three partsAdvectionForcePressure
Correct within a factor of O(Δt)
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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
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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
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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
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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]
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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.
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Particle InteractionsInteractions of liquids look
something like
Mathematically we model this with:
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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
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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
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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
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Smoothed Particle HydrodynamicsDemos
Simple SPH DemoAdding air particles
Boiling Pouring
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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
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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
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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
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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
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Texture SynthesisUsed at UNC for generating realistic textures
for dynamic fluidsVideo
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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
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Part II: Bubble Sound
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Cavitation InceptionTensile Strength Cavitation Nuclei
InsideVacuumGasVapor
Spherical Bubble
pi=pg+pv
ps
pL
R
p0
Hydrostatic pressure
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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
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Rayleigh-Plesset EquationR-P eq.
Work done by pressure difference =Kinetic Energy (Speed of wall)+ Viscosity damping μ+ (Acoustic radiation)+ (Thermal damping)
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Linearization of R-P eq.R-P eq. is non-linearLinearization for R = R0+r
Solution without damping
Minnaert Resonance Frequence
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DampingDamped Solution
Shifted resonance freq.
Damping factor
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DampingRadiation
Viscosity
Thermal
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Shifted Resonant Frequency
Large Bubble Assumption R > 0.1 mm, safely use Minnaert Fr
eq. 20hz ~ 20000hz 0.15m ~ 0.15mm
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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
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Experiments
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Nonspherical Bubble OscillationsSpherical Harmonics
Related to Oscillation modes
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BurstBefore burst
ThinningInstabilityInterference
magnifiedMove around
very fast.
Burst when wall is still much thicker than 10 nm, the barrier
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More IssueObstructionChange in Speed of SoundCouplingPopping excitation.
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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.