Mode-Splitting for Highly Detail, Interactive Liquid Simulation

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Mode-Splitting for Highly Detail, Interactive
Liquid Simulation
H. Cords University of Rostock
Presenter Truong Xuan Quang
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Content

• 0. Abstract
• Introduction
• 2. Related work
• 3. Our Approach
• 4. Implement and Result

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Abstract

• A new technique for highly detailed interactive
  liquid simulation
• Separated low-frequency (LF) and high-frequency
  (HF)
• LF free surface wave, 2D wave equation
• HF liquid follow, 3D Navier-Stock equation
• Rendering in 2.5 D
• Simulation liquid follow according to gravity,
  ground, obstacles and interaction with impacts,
  moving impact, etc

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Introduction

• Real-time liquid simulation can be classified as
  follows

• Empirical (expert) surface simulation
• Physically-based surface simulation
• (wave equation)
• Physically-based volume simulation
• (Navier-Stokes equations )

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Introduction

• The Goal mode-splitting to increase quality of
  the simulate liquid.
• Moving obstacles, rain, surface wave generation,
  etc
• Splitting based
• Navier-Stockes based method Fluid flow, movement
  of free surface
• 2D wave equation fast solve wave equation
• Finally combines the advantages of both
  physically-based approaches
• Limitation not valid in splashing or breaking
  wave

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Related work

• Simulation and rendering liquids and effected
  (e.g. Carlson et al. 2004 Hong and Kim 2005
  Guendelman et al. 2005 Muller et al. 2005).
• The Navier-Stokes equations are usually solved
  with particle-based systems (e.g Smoothed
  Particle Hydrodynamics - SPH), Adabala and
  Manohar 2002.
• In Stam and Fiume 1995 the first real-time
  approach using SPH is presented.
• Interactive simulation of fluids was introduced
  in Stam 1999
• Execution on the GPU with reasonable frame rates
  Harris-2005
• Solving the wave equation was presented Yuksel
  et al. 2007
• And etc..

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Our Approach

• Goal for simulation real-time and large scale
• Lagrangian methods few particles
• Liquid volume Small grid size (Eulerain)
• Propose model-slitting method to simulate highly
  detailed surface described by 2D wave equation
  is solve by FDM and liquid flow by Navier-Stockes
  equations there is solve with the (SPH)

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Our Approach
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Our Approach

• For visualization we use a height field-based
  rendering approach most liquid surface can be
  rendered appropriately as height fields.
• However, complex liquid phenomena, such as
  breaking waves or splashes, cannot be visualized
  as height fields.

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Mode Splitting
c speed of light l amplify frequency Nth mode

• Using oceanography the method is used to
  simulated high frequency waves is external
  gravity waves-included by tide and atmospheric
  pressure, water waves, free surface water.
• And low frequency waves Internal gravity wave
  included by wind and density gradients, vertical
  turbulences.
• Different algorithms are used, external and
  internal algorithms are solved separately with
  different time steps

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Mode Splitting

• Moving external waves need to be solved at small
  time steps
• The slow moving internal waves are more expensive
  to solve (due to complex turbulences), large time
  step can be used
• We used the 2D equation for surface simulation
  and a 3D SPH-based Navier-Stokes equations solver
  for volume flow simulation

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Surface simulation
The general wave equation describes the
propagations of wave in time t and space x,
liquid surface wave the 2D Wave equation can be
used, describing the circular wave Propagation
Laplace operator in 2D and c is the velocity at
the which wave propagate across The wave equation
can be solved with Eulerian finite difference
approach
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Implicit different method
a is constant, mgt0 is integer and time step
size kgt0, with hl/m
for each i0, 1, m
for each i0, 1, m
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Implicit different method
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Implicit different method
1. Several radius wave propagations 2. Rain-Drop
3. A swimming object is moving
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Liquid simulation
Navier-Stokes equations
V is velocity filed ? the pressure field µ
viscosity f external force
Conservation of mass (continuity equation ) in
rest position
Incompressible liquids, density is constant
Resulting in the mass conservation
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SPH for real-time simulation

• Simple and fast handling of boundary conditions
  as collisions
• Mass conservation is guaranteed (number of
  particles const mass of each particle const)
• Nonlinear convective acceleration
  can be neglected

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SPH
SPH (Smooth Particle Hydro-dynamics) is an
simulation method for particle systems defined
at discrete particle locations can be evaluated
everywhere in the space.
Continuous field quantities distributed in the
local neighborhood according to the discrete
particle positions and the smoothing kernels
Wh(x).
Scalar quantities A(x) can be estimated for n
particles as
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SPH
Smoothing kernel for pressure and viscosity
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SPH
The liquid volume is discredited by particles
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SPH
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Collisions

• Collisions of liquids particles with objects are
  using a force vector field surrounding collision
  objects

Where d is the closet distance between object and
particle nObject is normal vector of the object
at the points closet object Fcol is acting on
each particle being close to collision
objects V reflect velocity, friction
coefficient
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Free surface Extraction

• Generated height surface number of neighbors
  potential F for n particles with position xi
  (i1..n) is determined by the following spherical
  potential
• These particles can be detected according to
  their actual number of neighbors
• Threshold (condition of the smoothness), to
  reduce unwanted surface ripples cause by the
  discrete sampling of the liquids

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Free surface Extraction (2/2)

• Depending kinetic energy

n particles vi velocities mi mass (i1..m)
If Ekin exceeds a defined of threshold, no
smoothing occurs Else bellow threshold, the
number of smoothing steps is increased, until
the Maximum number of smoothing step is reach
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Simulation time-steps

• Surface simulation (wave equation) and volume
  simulation (SPH) should be synchronized

Example of time step (TS) Synchronization,
Ntime3 WE is solved 3 times, while Navier-Stockes
is solve once
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Combine surface and volume simulation

• Final surface just depends on the different field
  resolution
• SPH generated surface Xsph x Ysph
• Wave equation surface size XWE x YWE

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Rendering (1/2)

• Using cube map contain the environment for
  approximating the effects.
• Surface variation (position and normal)
  calculating reflection and refraction vectors.
• Reflection and refraction is described by
  Fresnel equation.

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Rendering (2/2)

• Planar light map is generated via light ray
  tracing using Snells law
• Other liquid can be also applied, simple liquid
  like
• milk, cola, oil.

WE
SPH
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4.1 Implementation and Results

• Using OpenGL 2.0 and shading language GLSL in
  C, dual core PC 2.6 GHz AMD Athlon 64 CPU.
• 2 GBs of RAM and graphics card ATIRadeon x 1900
  GPU.
• Using Parallel implementation with one core
  simulation SPH and one core solving wave equation

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4.1 Implementation and Results

• Performance of the technique mainly depend on the
  following parameter
• Number of SPH particles
• XSPH . YSPH
• XWE . YWE
• Results of experiments show that SPH simulation
  account for 40-70 of the run time-less than 4000
  particles.
• Disadvantage is impossible to visualize 3D liquid
  effects like splashes, breaking waves, cause by
  2.5D rendering approach
• (2D WE 3D SPH rendering)2.5D

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4.1 Implementation and Results

• Advantaged
• Volume interaction (moving glass of water,
  obstacles)
• Surface interaction (rain, moving objects)
• Automatic, natural and global flow
• Object moving with the follow
• Simulation pool or sea

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4.2 Conclusion and future work

• Simulation of the low frequency liquid flow and
  the high frequency free surface waves are
  separated
• 2D WE and 3D fluid (SPH-method) presented
  realistic and highly detailed results
• Future works
• Simulation in real-time environments at high
  frame rates, better rendering approach.
• GPU or PPU (Physic Processing Unit) for physical
  calculations.
• Applied for larger liquid volume

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Thank for your attention