An Efficient Particle Model for Viscous Liquids

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An Efficient Particle Model for Viscous
Liquids David Cline, Kevin Steele, Parris Egbert
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Our model Particles are used to simulate viscous
liquid flows. Each particle represents a small
volume of fluid, or a piece of a solid
object. The particle system evolves through
time, as gravity and inter-particle forces are
applied to particles. Forces are applied at
regular time intervals to all the fluid
particles. The net force on a particle in a time
step is the sum of all the forces acting on it
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• The forces acting on the particles
• Gravity
• Adhesion
• Viscosity
• Friction

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Gravity At each time step, a gravitational force
proportional to the time step is applied to
each fluid particle
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Adhesion To simulate forces between different
fluid types, our system uses a convenient
organization called the Adhesion Matrix. The
adhesion matrix contains an function defining
each type of adhesive interaction possible in the
simulation.
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Viscosity Viscosity is handled by performing a
momentum exchange between fluid particles.
Thus, in our system, viscosity is defined as a
rate of momentum exchange (how many times per
second a particle exchanges all its momentum with
its neighbors.) For a given time step, the
momentum exchange is given by
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Friction Solid objects are represented in our
system as collections of object particles.
When a fluid particle is touching an object
particle, a friction force is applied by
dampening the velocity of the fluid particle
relative to the velocity of the object particle.
For a single time step, this dampening is
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• Updating Positions after each time step
• Move the particles
• Prevent particle interpenetration
• Preserve volume

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Move the particles. At the end of each time
step, the particles are moved based on their
current velocity.
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Prevent Interpenetration At the end of each time
step, interpenetrating particles are pushed away
from each-other until they no longer
interpenetrate.
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Preserve Volume Because of the forces acting on
the fluid, the volume of the fluid invariably
changes over time. But most liquids we want to
simulate are incompressible! We apply an
iterative volume preservation algorithm after
each time step. The basic idea is that each
fluid particle calculates a local density measure
and then moves the neighbor particles away from
or toward itself to correct the local density.
No particle velocities are updated during this
step.
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Rendering The fluid particles are used to define
an implicit function. An iso-surface of the
implicit function given by the particles defines
the liquid surface.
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