Two-way coupling of fluids to reduced deformable bodies [electronic resource]

Reduced deformable bodies in the interactive and real-time applications have drawn a lot of attention from both the academy and the industry. It enables simulating a complex deformable model with restricted computational resources by exploiting the model reduction techniques. The results shown in the previous works are rather attractive. Yet, reduced deformable model still differs from other widely used physics-based simulation models, such as rigid model, mass-spring model, and finite element model, in its fundamental physical properties and the way it is formulated. These differences limit its applications, e.g. being used to model a free-flying object, full interaction between reduced deformable bodies and the fluids, and so on. In this dissertation, we reformulate the reduced deformable model with a projection-based momentum conserving impulse partition scheme, enabling the use of reduced deformable bodies as full-fledged simulation primitives alongside rigid bodies and deformable bodies. Momentum conservation is crucial to obtaining physically correct and realistic-looking motion in a fluid environment, and we achieve this by following previous work to describe reduced deformable bodies using both a rigid frame and a reduced space deformation component. Our approach partitions forces and impulses between the reduced space and the rigid frame of the reduced deformable bodies using a projection scheme that cleanly accounts for momentum losses in the reduced space via corrections in the rigid frame, resulting in a new theoretical formulation for the momentum-conserving reduced de- formable body. We demonstrate that robust and stable contact, collision, articulation, and two-way coupling with fluids are all attainable in a straightforward way using this new formulation. We then propose a fully monolithic two-way coupling framework that couples incompressible fluids to reduced deformable bodies. Our method allows for the simulation of interesting free-surface as well as underwater phenomena. Notably, the resulting linear system matrix is both symmetric and positive-definite. Compared with fully deformable objects, our framework consumes less memory and scales better in large scenes, while still nicely approximating the deformation effects. We demonstrate the robustness and efficacy of our framework by various examples including large scale ones. v In the end of this dissertation, we discuss reduced fluid simulation techniques that are preferable in the coupling with the reduced deformable model. In addition, we present an efficient grid structure that extends a uniform grid to create a significantly larger far-field grid by dynamically extending the cells surrounding a fine uniform grid while still maintaining fine resolution about the regions of interest. The far-field grid preserves almost every computational advantage of uniform grids including cache coherency, regular subdivisions for parallelization, simple data layout, the existence of efficient numerical discretizations and algorithms for solving partial differential equations, etc. This allows fluid simulations to cover large domains that are often infeasible to enclose with sufficient resolution using a uniform grid, while still adaptively allocate enough degrees of freedom in regions of interest to be coupled the reduced deformable model, and to capture fine scale details.

Advisor: Fedkiw Ronald P.
Savarese Silvio advisor. Thesis advisor
Zhu Bo