UCSD CSE 291D SP19

Author: Ziqi Gan

Project: Particle Based Fluids

Features

This project implements:

Basic SPH Solver

• Algorithm 1 from "SPH Fluids in Computer Graphics"
• Calculate pressure force explicitly with state equations.

For all particles:
  Find neighbors
For all particles:
  compute density
For all particles:
  compute presssure force
  compute viscosity force
  compute other forces (e.g. gravity)
  add them up
For all particles:
  update velocity
  update position

• Pros: Easy to implement.
• Cons:
  • Unstable
  • Small time step.

Acceleration Structure

For faster neighborhood search I implemented a uniform grid.

• The simulation space is divided into small cubic cells.
• Each particle is associated with one of the cells.
• The cell length equals to the support radius of the kernel.
• For each particle, loop through 3^3 = 27 cells to find all its neighbors.

Divergence Free Solver

• Solve pressure force implicitly.
• Predict particle velocities with non-pressure forces and iteratively correct density and divergence error.
• Divergence free solver is used to correct velocity field.
• Constant density solver to correct numerical errors.
• Simulation Step:

For all particles:
  find neighbors
For all particles:
  calculate densities and some factors

while(t < t_max):
  For all particles:
    calculate non-pressure forces.
  Calculate adaptive time step using CFL condition
  For all particles:
    predict velocities with calculated time step
  correct density error
  For all particles:
    predict position
  For all particles:
    find neighbors
  For all particles:
    calulate densities and some factors
  Correct divergence error
  For all particles:
    update velocities

• Pros:
  • Stable
  • Adaptive time step for faster update
• Cons:
  • Difficult to implement. Have to set up initial conditions carefully.

High Viscosity Fluid

The DFSPH paper also introduces an implicit viscosity solver.

• Viscosity tensor is defined by the strain rate tensor and the viscosity coefficient.
• Similar approach as the divergence and density solver.
• Iteratively compute the predicted strain rate, comparing it with the target strain rate, and correct velocities.
• Pros: Easy to intergrate with the divergence free solver.
• Cons:
  • Viscosity parameter depends on the time step. Not physically meaningful.
  • Solving the inverse of a six-dimentional matrix for each constriant, causing a large computional effort.
  • Extremely difficult to set up initial conditions.
    • Fixed time step: 1ms
    • particle radius: 0.025m

Air-Fluid Interaction

External Libraries

1. OpenGL Bindings: GLEW, GLFW .
2. Math: GLM, Eigen .
3. Search: CompactNSearch .
4. GUI: AntTweakBar .
5. Parallelism: OpenMP .

References

• "SPH Fluids in Computer Graphics", Ihmsen, Orthmann, Solenthaler, Kolb, Teschner
• Jan Bender and Dan Koschier. Divergence-free SPH for incompressible and viscous fluids. IEEE Transactions on Visualization and Computer Graphics, 2017.
• Miles Macklin, Matthias Müller, Nuttapong Chentanez and Tae-Yong Kim. Unified Particle Physics for Real-Time Applications. ACM Trans. Graph., 33(4), 2014