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Fluid simulation is becoming increasingly common in the film industry and in computer games, however, understanding and implementing a numerical solution to the Navier-Stokes equation can be a daunting task. In this thesis we present an introduction to fluid simulation in computer graphics with a full derivation of the compressible and incompressible Navier-Stokes equation from Newton's Second Law, explaining concepts such as pressure and viscosity as they are derived. We also present a survey and comparison of four different methods for solving the advection equation: a simple 1st order differencing method, a 4 th order QUICK scheme, the popular semi-lagrangian method, and the PIC & FLIP particle based methods. We present these advection scheme comparisons in a series simplified 1D channel plots, and a set of 2D fluid animations. Based on these results, we classify algorithms as stable or unstable, and discuss methods to prevent divergence in unstable solvers.
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Advisor: | Jensen, Henrik Wann |
Commitee: | Buss, Samuel R., Zwicker, Matthias |
School: | University of California, San Diego |
Department: | Computer Science and Engineering |
School Location: | United States -- California |
Source: | MAI 46/05M, Masters Abstracts International |
Source Type: | DISSERTATION |
Subjects: | Computer science |
Keywords: | Computer graphics, Fluid simulation, Navier-Stokes |
Publication Number: | 1450292 |
ISBN: | 978-0-549-46270-5 |