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Full-Text Articles in Physical Sciences and Mathematics
Numerical Simulations Of Thin Viscoelastic Films, Valeria Barra
Numerical Simulations Of Thin Viscoelastic Films, Valeria Barra
Dissertations
This dissertation is developed in the field of Computational Fluid Dynamics (CFD) and it focuses on numerical simulations of the dynamics of thin viscoelastic films in different settings. The first part of this dissertation presents a novel computational investigation of thin viscoelastic films and drops, that are subject to the van der Waals interaction force, in two spatial dimensions. The liquid films are deposited on a flat solid substrate, that can have a zero or nonzero inclination with respect to the base. The equation that governs the interfacial dynamics of the thin films and drops is obtained within the long-wave …
A New Finite Difference Time Domain Method To Solve Maxwell's Equations, Timothy P. Meagher
A New Finite Difference Time Domain Method To Solve Maxwell's Equations, Timothy P. Meagher
Dissertations and Theses
We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component, Er(x,y), …
Numerical Solutions Of Fractional Nonlinear Advection-Reaction-Diffusion Equations, Sophia Vorderwuelbecke
Numerical Solutions Of Fractional Nonlinear Advection-Reaction-Diffusion Equations, Sophia Vorderwuelbecke
Theses and Dissertations
In this thesis nonlinear differential equations containing advection, reaction and diffusion terms are solved numerically, where the diffusion term is modelled by a fractional derivative. One of the methods employed is a finite difference method for temporal as well as spatial discretization. Furthermore, exponential time differencing schemes under consideration of different matrix exponential approximations are exploited for the temporal discretization, whereas finite differences are used for the spatial approximation. The schemes are applied to the homogeneous Burgers, Burgers-Fisher and Burgers-Huxley equation and compared with respect to convergence and efficiency in a numerical investigation.