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We investigate the asymptotic behaviour of the wetting front arising from unsaturated flow in porous media wherein the liquid saturation θ obeys a nonlinear diffusion equation having moisture diffusivity that is an exponential function D(θ) = Do exp(βθ). For values of the physical parameters corresponding to actual porous media, the diffusivity at the(More)
The immersed boundary method is known to exhibit a high degree of numerical stiiness, which is associated with the interaction of immersed elastic bres with the surrounding uid. We perform a linear analysis of the underlying equations of motion for immersed bres, and identify a discrete set of bre modes which are associated solely with the presence of the(More)
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The Gaussian plume model is a standard approach for studying the transport of airborne contaminants due to turbulent diffusion and advection by the wind. This paper reviews the assumptions underlying the model, its derivation from the advection-diffusion equation, and the key properties of the plume solution. The results are then applied to solving an(More)
We accept this thesis as conforming to the required standard In presenting this thesis in partial fullllment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive c o p ying of this thesis for scholarly(More)
In this paper, we investigate a traffic model similar to the Lighthill–Whitham– Richards model, consisting of a hyperbolic conservation law with a discontinuous, non-convex, piecewise-linear flux. Using Dias and Figueira's mollification framework, analytical solutions to the corresponding Riemann problem are derived. For certain initial data, these Riemann(More)
We present an approach for numerically simulating the dynamics of flexible fibers in a three-dimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev's pseudo-compressible fluid solver. The fibers are treated as one-dimensional Kirchhoff rods that resist stretching, bending, and twisting, within the generalized IB(More)