Level set methods: an overview and some recent results

We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging to invert. The semi-Lagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.

/pdf/simulating-water-and-smoke-with-an-octree-data-structure-3cgy6zahqn.pdf

Simulating water and smoke with an octree data structure

http://physbam.stanford.edu/~fedkiw/papers/cam2000-37.pdf

A second-order-accurate symmetric discretization of the Poisson equation on irregular domains

https://www.math.fsu.edu/~sussman/twofluid.pdf

A sharp interface method for incompressible two-phase flows

https://jupiter.math.nctu.edu.tw/~mclai/papers/Lai_3.pdf

The immersed interface method for the Navier-Stokes equations with singular forces

We present a physically based method for modeling and animating fire. Our method is suitable for both smooth (laminar) and turbulent flames, and it can be used to animate the burning of either solid or gas fuels. We use the incompressible Navier-Stokes equations to independently model both vaporized fuel and hot gaseous products. We develop a physically based model for the expansion that takes place when a vaporized fuel reacts to form hot gaseous products, and a related model for the similar expansion that takes place when a solid fuel is vaporized into a gaseous state. The hot gaseous products, smoke and soot rise under the influence of buoyancy and are rendered using a blackbody radiation model. We also model and render the blue core that results from radicals in the chemical reaction zone where fuel is converted into products. Our method allows the fire and smoke to interact with objects, and flammable objects can catch on fire.

/pdf/physically-based-modeling-and-animation-of-fire-27xrar3et7.pdf

Physically based modeling and animation of fire

http://physbam.stanford.edu/~fedkiw/papers/cam2000-19.pdf

A boundary condition capturing method for incompressible flame discontinuities

In this paper, we present an efficient method for simulating highly detailed large scale participating media such as the nuclear explosions shown in figure 1. We capture this phenomena by simulating the motion of particles in a fluid dynamics generated velocity field. A novel aspect of this paper is the creation of highly detailed three-dimensional turbulent velocity fields at interactive rates using a low to moderate amount of memory. The key idea is the combination of two-dimensional high resolution physically based flow fields with a moderate sized three-dimensional Kolmogorov velocity field tiled periodically in space.

/pdf/smoke-simulation-for-large-scale-phenomena-3xzvrq19tt.pdf

Duc Quang Nguyen

Papers

Physically based modeling and animation of fire

A boundary condition capturing method for incompressible flame discontinuities

Smoke simulation for large scale phenomena