Digital marbling based on computational fluid dynamics

This thesis addresses the problem of using computational fluid dynamics techniques for artistic simulation purposes in computer graphics. Marbling is a traditional art of abstract painting which makes use of the dynamics of fluid flow. It involves complex physical and chemical processes, some of which have not even been investigated in conventional fluid dynamics. Inspired by the complexity and variety of traditional marbling patterns, and based on an analysis of the physical aspects of the marbling techniques, a generic tool has been developed that can be used to simulate a wide range of flows from the very viscous to the highly turbulent. Considering the numerical requirements for certain problems in fluid modeling, the digital marbling problem is first divided into two parts: the fluid model and the transport model. The fluid model involves solving the fluid equations; it consists of two parts. The first part constitutes a multiscale model based on mesoscale dynamics and viscous fluid equations; it allows for various user control to simulate complex flow behaviours as in traditional marbling techniques as well as laminar and turbulent flows. The second part is based on a solution of inviscid equations; it is used to simulate vortex sheet dynamics, turbulence, and other artistic effects (including some well-known marbling techniques). The transport model describes the material transport throughout the velocity space. It includes an interface model and two reaction models to simulate certain characteristics of marbling flows as well as other artistic effects.