Numerical Approximation of Partial Differential Equations
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In this thesis we address the numerical approximation of the incompressible Navier-Stokes equations evolving in a moving domain with the spectral element method and high order time integrators. First, we present the spectral element method and the basic to ...
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Mailapalli et al. (2009) presented an explicit numerical scheme for calculation of solutions to the 1D Green and Ampt (1911) infiltration equation. They compared their numerical solution to a numerical solution obtained using the Newton-Raphson method (e.g ...
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as w ...
The scaling of turbulence-driven heat transport with system size in magnetically confined plasmas is reexamined using first-principles based numerical simulations. Two very different numerical methods are applied to this problem, in order to resolve a long ...
Ordinary differential equations are coupled with mixed constrained optimization problems when modeling the thermodynamic equilibrium of a system evolving with time. A particular application arises in the modeling of atmospheric particles. Discontinuity poi ...
The divergence of the theory and practice of vocal tract length normalization (VTLN) is addressed, with particular emphasis on the role of the Jacobian determinant. VTLN is placed in a Bayesian setting, which brings in the concept of a prior on the warping ...
