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Title: Fast fluid simulation in computer graphics using Fourier theory
Author: Long, Benjamin
ISNI:       0000 0004 2722 8136
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2011
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Fluid simulation techniques are computationally expensive and are required to visualise physical phenomena in virtual and augmented environments. In order to realise such simulations, a discretisation is constructed and differ': ential equations applied. These yield predictive descriptions of the physical fluid stepped in time, which can be used for animation. Fast Fourier transforms can be used to significantly accelerate the most time consuming step of solving incompressible fluid equations, the incompress- ibility projection. However, using fast Fourier transforms means accepting their inherent weaknesses; preset periodic boundary conditions, homogeneous treatment of equation coefficients and behaviour limited to solution over uni- form rectilinear grids. Fourier transforms also have intrinsic links to the theoretical structure of perfect fluids through energy spectra and statistics. Through Fourier analysis the frequency space structure of differential operators can be studied and optimised towards the preservation of stability and damping of unwanted simulation artifacts. This thesis is concerned with using both the practical and theoretical sides of Fourier transform theory to author new fluid simulation methods. The accel- eration that fast Fourier transforms 'provide in simulations can be obtained in such a way that inherent weaknesses are not encountered and that corre- sponding advantages are maximally exploited. Using Fourier transforms as a basis for fast simple fluid simulations, this thesis proposes new algorithms which build approximations of more complex scenarios on top of these sim- ulations, yielding the visual effects of these complex phenomena, but at a fraction of the computational cost. This includes algorithms for multi phase flows and arbitrarily bounded fluids including deformable objects. These approximate schemes have a two orders of magnitude reduction in computa- tional time with respect to the state-of-the-art in simulating these effects. The theoretical connections of Fourier transforms are also used to create a new technique for solving partial differential equations using both statis- tical and spatial information. Using Fourier theory in this way elucidates connections between covariance functions and finite difference convolutions, enabling the use of fast linear system solvers to find solutions to differential equations expressed over particle systems. With the use of these techniques that were previously reserved only for rigid grid based differential equation solutions, substantial improvements in reliability and speed for this class of problem are shown.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available