Signorini conditions for inviscid fluids
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Date
2021-06-28
Authors
Gu, Yu
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
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.
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Keywords
computer graphics, fluid simulation, numerical algorithm, finite element method, elliptic PDEs
LC Keywords
Computer graphics, Finite element method, Computer programs