The particle level set method has proven successful for the simulation of two separate regions (such as water and air, or fuel and products). In this paper, we propose a novel approach to extend this method to the simulation of as many regions as desired. The various regions can be liquids (or gases) of any type with differing viscosities, densities, viscoelastic properties, etc. We also propose techniques for simulating interactions between materials, whether it be simple surface tension forces or more complex chemical reactions with one material converting to another or two materials combining to form a third. We use a separate particle level set method for each region, and propose a novel projection algorithm that decodes the resulting vector of level set values providing a "dictionary" that translates between them and the standard single-valued level set representation. An additional difficulty occurs since discretization stencils (for interpolation, tracing semi-Lagrangian rays, etc.) cross region boundaries naively combining non-smooth or even discontinuous data. This has recently been addressed via ghost values, e.g. for fire or bubbles. We instead propose a new paradigm that allows one to incorporate physical jump conditions in data "on the fly," which is significantly more efficient for multiple regions especially at triple points or near boundaries with solids.

Multiple interacting liquids

This thesis presents a model of woven cloth that is capable of reproducing the draping behavior of a variety of fabrics. Here, draping behavior means the final draped configuration of a cloth, consisting of characteristic folds, over a solid object. The model utilizes a new approach, called particle-based modeling, to simulate the mechanical properties of complex materials. In contrast to continuum techniques, particle modeling is founded on the premise that by directly modeling the microstructures of a material and computationally aggregating their interactions correct macroscopic behavior will emerge. Cloth is not a continuous material, but rather a complex mechanism. Cloth's microstructure consists of threads interlaced in a particular weave pattern. Therefore, the model treats the thread crossing as the fundamental modeling unit, which is called a "particle". It is at the level of these particles that constraints are maintained, in the form of potential energy functions, on the relationships between the threads. The constraints maintained in the particle grid embody four basic mechanical interactions occurring in cloth at the thread level. They are thread collision, thread stretching, thread bending, and trellising.
An important feature of the model is that its thread-relationship constraints can be defined to simulate specific types of woven materials. This is accomplished by deriving the model's energy functions from empirical mechanical data produced from a standard set of fabric measurement equipment, the Kawabata Evaluation System. Given this capability, a woven material may be measured on the Kawabata System, and a model with the material's mechanical properties may then be defined to confidently simulate its draping behavior on a computer.
The validity of the model has been verified by performing two experiments with three different kinds of woven cloth. The first experiment recreates in simulation the standard measurement procedures that are applied to cloth and produces simulated mechanical data. The second experiment performs controlled draping experiments with real cloth, then recreates those experiments with draping simulations utilizing the model. This experiment demonstrates that the model is capable of reproducing the unique large-scale draping structures present in each of the experimental samples.

A particle-based model for simulating the draping behavior of woven cloth

A three-dimensional computational model is developed for simulating the flag motion in a uniform flow. The nonlinear dynamics of the coupled fluid–flag system after setting up of flapping is investigated by a series of numerical tests. At low Reynolds numbers, the flag flaps symmetrically about its centreline when gravity is excluded, and the bending in the spanwise direction is observed near the corners on the trailing edge. As the Reynolds number increases, the spanwise bending is flattened due to the decrease of the positive pressure near the side edges as well as the viscous force of the fluid. At a certain critical Reynolds number, the flag loses its symmetry about the centreline, which is shown to be related to the coupled fluid–flag instability. The three-dimensional vortical structures shed from the flag show a significant difference from the results of two-dimensional simulations. Hairpin or O-shaped vortical structures are formed behind the flag by connecting those generated at the flag side edges and the trailing edge. Such vortical structures have a stabilization effect on the flag by reducing the pressure difference across the flag. Moreover, the positive pressure near the side edges is significantly reduced as compared with that in the center region, causing the spanwise bending. The Strouhal number defined based on the flag length is slightly dependent on the Reynolds number and the flag width, but scales with the density ratio as St ~ ρ−1/2). On the other hand, the flapping-amplitude-based Strouhal number remains close to 0.2, consistent with the values reported for flying or swimming animals. A flag flapping under gravity is then simulated, which is directed along the negative spanwise direction. The sagging down of the flag and the rolling motion of the upper corner are observed. The dual effects of gravity are demonstrated, i.e. the destabilization effect like the flag inertia and the stabilization effect by increasing the longitudinal tension force.

Three-dimensional simulation of a flapping flag in a uniform flow

The integration of physics-based models within CAD systems for garment design leads to highly accurate cloth shape results for virtual prototyping and quality evaluation tasks. To this aim, we present a physics-based system for virtual cloth design and simulation expressly conceived for design purposes. This environment should allow the designer to validate her/his style and design option through the analysis of garment virtual prototypes and simulation results in order to reduce the number and role of physical prototypes. Garment shapes are accurately predicted by including material properties and external interactions through a particle-based cloth model embedded in constrained Newtonian dynamics with collision management, extended to complex-shaped assembled and finished garments. Our model is incorporated within a 3D graphical environment, and includes operators monitoring the whole design process of apparel, e.g. panel sewing, button/dart insertion, multi-layered fabric composition, garment finishings, etc. Applications and case studies are considered, with analysis of CAD modelling phases and simulation results concerning several male and female garments.

3D virtual apparel design for industrial applications

This thesis is concerned with various computational aspects of surface dynamics. By this I mean algorithms and data structures to support simulations of the physics taking place on or about two-dimensional manifolds. This includes internal dynamics (e.g. elastic forces) and external dynamics (e.g. collisions). 
The core of the thesis is simulating cloth motion, including the internal elastic dynamics, the external dynamics of contact and collision, and post-processing of the data for rendering. The contact and collision algorithm, based on the notion of a collision resolution pipeline where candidate trajectories are passed through several stages designed to resolve different classes of collisions, was subsequently adapted to rigid body simulation. 
Surface dynamics are also potentially the most important part of simulations of deformable objects, driving the deformation of the interior. Chapter 5 presents a tetrahedral mesh generation algorithm designed to support large surface deformations. Adaptivity is also discussed. 
Throughout the thesis implicit surfaces defined by level sets are used to represent geometry. Level sets are used in many other areas, especially computational fluid dynamics for simulations of the surface between distinct regions of flow (e.g. material boundaries). Their chief drawback is storage expense. Chapter 6 presents a data structure for efficiently storing level sets without needing to change algorithms designed for regular grids. An example application, an interactive sculpting tool, is presented to illustrate the structure.

Computational aspects of dynamic surfaces

This paper is focused on the analysis of the intersection between the air-flow field around a piece of cloth and the motion of the cloth in order to animate realistically the cloth motion in the air flow. Two force models, based on aerodynamic theory, have been established to calculate the force distribution of the air flow on a cloth surface. The quasi-steady force model deals with the cases in which the free stream velocity of the relative air flow changes slightly or slowly, whereas the unsteady force model deals with unsteady air flows. The resulting force distributions are coupled with a cloth-deformation model based on structural dynamics to compute the displacement and deformation of cloth under these forces. This solution cycle is repeated and the time histories of the cloth motion can be obtained which form the basis of the computer animation of cloth motion in air flow. Animation results of the movement of a piece of curtain in free air under various air flow conditions are presented to compare the performances of the two force models.

Aerodynamic force models for animating cloth motion in air flow

A Quasi-steady Force Model for Animating Cloth Motion

Publisher Summary This chapter describes physical modeling for animating cloth motion. Computer animation of cloth motion has implications for many graphics applications. In this chapter an approximate physics-based model is proposed for obtaining realistic animation of cloth motion for computer graphics applications. The model is constructed based on concepts from structural dynamics and low-speed wing aerodynamic theories with some modifications. Concepts from low-speed unsteady aerodynamic theory of wings coupled with proper boundary conditions to account for the porosity of cloth and the effects of the presence of boundaries such as walls near a moving piece of cloth are used to estimate the unsteady force distributions on the cloth surface which is assumed to be in motion in free air. The motivation for using aerodynamic theory is to model a distributed force model as opposed to using predefined concentrated force models, thereby incorporating some form of automatic control for the synthesis of the complex shapes the cloth can take and for obtaining realistic motion. These force distributions are then used in a cloth deformation model to estimate the displacements of various points of the cloth at different instants of time.

Physical modelling for animating cloth motion

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Aerodynamic force models for animating cloth motion in air flow

A Quasi-steady Force Model for Animating Cloth Motion

Physical modelling for animating cloth motion