Coupled simulation of deformable solids, rigid bodies, and fluids with surface tension [electronic resource]

This thesis considers the numerical simulation of a variety of phenomena, particularly rigid bodies, deformable bodies, and incompressible fluids. We consider each of these simulations types in isolation, addressing challenges specific to each. We also address the problem of monolithic two-way coupling of each of these phenomena. First we address the stability of rigid body simulation with large time steps. We develop an energy correction for orientation evolution and another correction for collisions. In practice, we have found these two corrections to be sufficient to produce stable simulations. We also explore a simple scheme for rigid body fracture that is as inexpensive as prescoring rigid bodies but more flexible. Next we develop a method for simulating deformable but incompressible solids. Many constitutive models for deforming solids, such as the neo-Hookean model, break down in the incompressible limit. Simply enforcing incompressibility per tetrahedron leads to locking, where the mesh non-physically resists deformation. We present a method that uses a pressure projection similar to what is commonly used to simulate incompressible solids and apply it to deforming solids. We also address the complications that result from the interaction of this new force with contacts and collisions. Then, we turn to two coupling problems. The first problem is to couple deformable bodies to rigid bodies. We develop a fully-unified time integration scheme, where individual steps like collisions and contact are each fully two-way coupled. The resulting coupling scheme is monolithic with fully coupled linear systems. This leads to a robust and strongly coupled simulation framework. We use state-of-the-art integrators for rigid bodies and deformable bodies as the basis for the coupling scheme and maintain the ability to handle other phenomena, such as articulation and controllers on the rigid bodies and incompressibility on the deformable bodies. We follow this up by developing a scheme for coupling solids to incompressible fluids. The method handles both deformable bodies and rigid bodies. Unlike many existing methods for fluid structure interaction, which often typically lead to indefinite linear systems, the developed scheme results in a symmetric and positive definite (SPD) linear system. In addition to strongly coupling solids and fluids, the method also strongly couples viscosity with fluid pressure. This allows it to accurately treat simulations with high viscosity or where the primary coupling between solid and fluid is through fluid viscosity rather than fluid pressure. The method can be interpreted as a means of converting symmetric indefinite KKT systems with a particular form into SPD systems. Finally, we propose a method for applying implicit Lagrangian forces to an Eulerian Navier-Stokes simulation. We utilize the SPD framework to produce an SPD system with these implicit forces. We use this method to apply implicit surface tension forces. This implicit surface tension treatment reduces the tight time step restriction that normally accompanies explicit treatments of surface tension.

Advisor: Fedkiw Ronald P.
Anderson John advisor. Thesis advisor
Khatib Oussama advisor. Thesis advisor