Fluid Simulation for Computer Graphics

THE BASICS The Equations of Fluids Symbols The Momentum Equation Lagrangian and Eulerian Viewpoints Incompressibility Dropping Viscosity Boundary Conditions Overview of Numerical Simulation Splitting Splitting the Fluid Equations Time Steps Grids Dynamic Sparse Grids Two Dimensional Simulations Advection Algorithms Semi-Lagrangian Advection Boundary Conditions Time Step Size Diffusion Reducing Numerical Diffusion Level Set Geometry Signed Distance Discretizing Signed Distance Functions Computing Signed Distance Recomputing Signed Distance Operations on Level Sets Contouring Limitations of Level Sets Extrapolating Data Making Fluids Incompressible The Discrete Pressure Gradient The Discrete Divergence The Pressure Equations Projection More Accurate Curved Boundaries The Compatibility Condition Smoke Temperature and Smoke Concentration Buoyancy Variable Density Solves Divergence Control Particle Methods Advection Troubles on Grids Particle Advection Transferring Particles to the Grid Particle Seeding Diffusion Particle-in-Cell Methods MORE TYPES OF FLUIDS Water Marker Particles and Voxels More Accurate Pressure Solves Topology Change and Wall Separation Volume Control Surface Tension Fire Thin Flames Volumetric Combustion Viscous Fluids Stress Applying Stress Strain Rate and Newtonian Fluids Boundary Conditions Implementation MORE ALGORITHMS Turbulence Vorticity Vorticity Confinement Procedural Turbulence Simulating Sub-Grid Turbulence Shallow Water Deriving the Shallow Water Equations The Wave Equation Discretization Ocean Modeling Potential Flow Simplifying Potential Flow for the Ocean Evaluating the Height Field Solution Unsimplifying the Model Wave Parameters Eliminating Periodicity Vortex Methods Velocity from Vorticity Biot-Savart and Streamfunctions Vortex Particles Coupling Fluids and Solids One-Way Coupling Weak Coupling The Immersed Boundary Method General Sparse Matrices Strong Coupling Background Vector Calculus Numerical Methods Derivations The Incompressible Euler Equations