Simulation of fluids with reduced diffusion, thin liquid films, volume control, and a mesh filter in rational form

Abstract

This thesis is concerned with the evolution of implicit or explicit surfaces.

The first part of this thesis addresses three problems in fluid simulation: advection, thin film, and the volume error. First, we show that the back and forth error compensation and correction (BFECC) method can significantly reduce the dissipation and diffusion. Second, thin film is hard to simulate since it has highly complex liquid/gas interface that requires high memory and computational costs. We address this difficulties by using cell centered octree grid to reduce memory cost and a multigrid method to reduce computational cost. Third, the volume loss is an undesired side effect of the level set method. The known solution to this problem is the particle level set method, which is expensive and has small but accumulating volume error. We provide a solution that is computationally effective and can prevent volume loss without accumulation.

The second part of this thesis is focused on filtering a triangle mesh to produce a mesh whose details are selectively reduced or amplified. We develop a mesh filter with a rational transfer function, which is a generalization from previously developed mesh filters. In addition, we show that the mesh filter parameters can be computed from the physical size of mesh feature.