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Robust and Efficient Wave Simulations on Deforming Meshes
Author(s) -
Angst Roland,
Thuerey Nils,
Botsch Mario,
Gross Markus
Publication year - 2008
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2008.01337.x
Subject(s) - polygon mesh , computer science , solver , integrator , robustness (evolution) , computational science , generality , dissipation , sbml , mathematical optimization , algorithm , mathematics , computer graphics (images) , psychotherapist , gene , programming language , thermodynamics , psychology , computer network , biochemistry , chemistry , physics , operating system , markup language , xml , bandwidth (computing)
The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real‐time environments. In order to achieve our goal, we reduce the problem from a three‐ to a two‐dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.