Grid-based methods have difficulty resolving features on or below the scale of the underlying grid. Although adaptive methods (e.g. RLE, octrees) can alleviate this to some degree, separate techniques are still required for simulating small-scale phenomena such as spray and foam, especially since these more diffuse materials typically behave quite differently than their denser counterparts. In this paper, we propose a two-way coupled simulation framework that uses the particle level set method to efficiently model dense liquid volumes and a smoothed particle hydrodynamics (SPH) method to simulate diffuse regions such as sprays. Our novel SPH method allows us to simulate both dense and diffuse water volumes, fully incorporates the particles that are automatically generated by the particle level set method in under-resolved regions, and allows for two way mixing between dense SPH volumes and grid-based liquid representations.
Month: December 2007
Level Set Driven Flows
In 2D, incompressible flows, the Stokes equations that represent the dynamics of very viscous flows and vorticity formulation of hydrodynamic equations both reduce to a scalar stream-function representation in terms of elliptic equations. By making use of this simplification and the properties of Fourier space representation of elliptic equations, we use a common spectral method to solve both of these equations. Based on this system of equations, we propose a level set based input description which provides a flexible environment for the user to model a wide range of flows and artistic effects in 2D. This input type allows the modeling of vortex sheet patterns and other complex flows with a very practical approach and chaotic, dynamic flows, even with viscous Stokes equations. A user interface is developed for the level set input which allows the user to draw the strokes or edit the level set data by applying transformation functions or perturbations. To sum up, this model can be used for the simulation of very viscous flows, vorticity dynamics, vortex sheet patterns, turbulent and chaotic flows as well as other artistic effects such as the traditional marbling patterns, with a simple, fast and stable system at high resolutions.