Signorini conditions for inviscid fluids

In this thesis, we present a new type of boundary condition for the simulation of inviscid fluids – the Signorini boundary condition. The new condition models the non-sticky contact of a fluid with other fluids or solids. Euler equations with Signorini boundary conditions are analyzed using variational inequalities. We derived the weak form of the PDEs, as well as an equivalent optimization based formulation. We proposed a finite element method to numerically solve the Signorini problems. Our method is based on a staggered grid and a level set representation of the fluid surfaces, which may be plugged into an existing fluid solver. We implemented our algorithm and tested it with some 2D fluid simulations. Our results show that the Signorini boundary cpndition successfully models some interesting contact behavior of fluids, such as the hydrophobic contact and the non-coalescence phenomenon

Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions

We propose and evaluate fast, scalable approaches for solving the linear complementarity problems (LCP) arising from the fluid pressure equations with separating solid boundary conditions. Specifically, we present a policy iteration method, a penalty method, and a modified multigrid method, and demonstrate that each is able to properly handle the desired boundary conditions. Moreover, we compare our proposed methods against existing approaches and show that our solvers are more efficient and exhibit better scaling behavior; that is, the number of iterations required for convergence is essentially independent of grid resolution, and thus they are faster at larger grid resolutions. For example, on a 256^3 grid our multigrid method was 30 times faster than the prior multigrid method in the literature