CSCI-6962 Advanced Computer Graphics, Fall 2005
Assignment 3: Flow Simulation

The goal of this assignment is to experiment with a (partially-implemented) 3D Flow Simulator for fluid, smoke, viscous materials, etc. The bulk of the implementation has been provided including data structures, a discrete approximation of the Navier-Stokes Equations, and some rendering tools.

Some implementation details in the code are incomplete and other things may be (unintentionally) incorrect. In this assignment you will implement velocity interpolation for marker particles, play with free-slip and no-slip boundary conditions for incompressible flows, compressible flows, and create your own new scene or visualization.

Tasks

• Download the provided source code below and the simple test datasets. Compile it on your favorite platform and try these sample command lines:

  fluid -grid 20 10 1 -size 600 -density 10 -timestep 0.05 -viscosity 0.1
  fluid -grid 20 10 1 -size 600 -density 50 -timestep 0.1 -viscosity 0.05
  fluid -grid 20 10 1 -size 600 -density 50 -timestep 0.2 -viscosity 0.01
  fluid -grid 10 7 10 -size 600 -density 10 -timestep 0.1 -viscosity 0.05
  
  fluid -input spiral_xy.txt -size 600 -gravity 0 -density 100
  fluid -input spiral_xz.txt -size 600 -gravity 0 -density 100
  fluid -input spiral_yz.txt -size 600 -gravity 0 -density 100
  

  Once the viewer is launched you can rotate the scene with the mouse, press "a" to begin or pause the animation, press "m" to turn on/off the marker particle rendering, press "v" to turn on/off the average cell velocity rendering, press "e" to turn on/off the cell face velocity rendering, press "s" to turn on/off the marching cubes surface, press "c" to visualize the MAC (Full, Empty, Surface) voxels, or press "p" to visualize the pressure. You can also edit the viscosity and timestep from the command line. See argparser.h and glCanvas.C for all the options or to add your own.

• You've probably noticed by now that the marker particle flow isn't particularly smooth or physically correct. It's time to dig into the code. I've marked sections you may want to edit with the string "ASSIGNMENT" and some comments in the files grid.h and grid.C. You'll probably want to spend a little time poking around the other files too.

  Look at the code to MoveParticles function. The implementation is using a simple cell-centered average for the particle velocity. Your first task is to implement the correct interpolation in 3D as described in the papers referenced in class:

  • Harlow, F.H., and E. Welch, "Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluids with Free Surface," Phys. Fluids, Vol. 8, p. 2182, 1965. (Paper copy distributed in class. Also available in Folsom library.)

  • Nick Foster and Dimitri Metaxas, Realistic Animation of Liquids (extended), Graphical Models and Image Processing, 58(5), (1996), pp. 471-483.

  NOTE: In the implementation provided, each cell stores the face velocities (u, v, & w) for the face it shares with the cell in the positive direction along each axis. That is, cell_i,j,k stores u_i+1/2,j,k, v_i,j+1/2,k, and w_i,j,k+1/2. These values are stored in the variables u_plus, v_plus, and w_plus, and the corresponding accessors get_u_plus(), get_v_plus(), and get_w_plus().

• Examine the code for enforcing incompressible flows. Add a command line option to control the degree of compressibility allowed within the simulation. For extra credit you can implement the free-slip and no-slip boundary conditions in the Marker and Cell (MAC) method. You probably want to focus on a 2D scene, at least initially. Describe any extensions in your README.txt file.

• Experiment with the provided Marching Cubes implementation. Try different isosurface values (a command line option and keyboard shortcut --- press '+'/'-') and render the isosurfaces of different scalar fields such as density or pressure or divergence (for compressible flows). Discuss in your README.txt file.

  If you're really motivated, increase the resolution of the grid before running marching cubes. You'll see in the implementation how each grid cell is divided into 8 cubes before polygonization. You can get a smoother surface if you subdivide further. And if you're extremely motivated, add gouraud shading to the marching cubes surface!

• Implement a new visualization/rendering mode (maybe you already did to debug an earlier step) -- OR -- create a new test environment (you can create it procedurally, or create a new input file). Describe your extension in your README.txt file. A fun test scene could include source and sink cells where mass is created and deleted or a spatial or time varying force field (instead of a uniform gravity).

• Finally, please document in your README.txt file and bugs you found (and hopefully fixed!) in the original code :)

Additional References

• Practical animation of liquids, Foster & Fedkiw, SIGGRAPH 2001

• Visual simulation of smoke, Fedkiw, Stam & Jensen, SIGGRAPH 2001

• "Melting and Flowing" Carlson, Mucha, Van Horn III & Turk, ACM SIGGRAPH Symposium on Computer Animation 2002

Basic Code, similar to previous assignments

• vectors.h
• matrix.h
• matrix.C
• camera.h
• camera.C
• glCanvas.h
• glCanvas.C
• Makefile
• argparser.h
• main.C
• utils.h
• bag.h
• boundingbox.h
• boundingbox.C

Fluid simulation and data structures

• particle.h
• cell.h
• grid.h
• grid.C
• marching_tetras.C

Simple test datasets

These files test your simulation in 2D perpendicular to each axis so you can check that you've got your indices sorted out correctly.

• spiral_xy.txt
• spiral_xz.txt
• spiral_yz.txt

CODE COMPILED IN VISUAL STUDIO 6.0(.tar.gz)

Please read the assignment information again before submitting.