Numerical algorithms are developed for compressible multicomponent flow problems in the framework of wave propagation finite volume methods based on approximate Riemann solvers. Both models for multifluid flows, which involve pure species separated by well-defined interfaces, and for two-phase flows made of gas carrying a ...

A widely-accepted technique for the analysis of rigid mechanical systems with unilateral contact and Coulomb friction is to formulate the contact forces (or impulses) as the unknowns of a linear complementarily problem (LCP). However, the solution set of an arbitrary LCP may be nonconvex, which poses the following computational ...

This thesis describes the Immersed Interface Method (IIM) for interface problems, in which the partial differential equations have discontinuities and singularities in the coefficients and the solutions. A typical example of such problems is heat conduction in different materials (discontinuous heat conductivity), or fluid ...

This dissertation investigates the general problem of reproducing color images on an off-set printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing with inks other than the standard process colors (cyan, magenta, yellow, and black), particularly as the ...

We study the behavior of solutions of certain parabolic partial differential equations of the form ut = epsilon2 uxx + epsilong(u) ux + h(u) in the limit epsilon → 0+. Solutions of advection-diffusion and reaction-diffusion equations are specifically considered. These solutions possess slowly moving internal layers, the ...

With water in short supply and utility deregulation imminent, the problem of long-term scheduling on a hydroelectric power system has become increasingly important.Many of the algorithms developed for this large-scale multistage stochastic problem have relied on the dynamic programming algorithm; and so have suffered from the ...

This thesis presents a new adaptive multilevel numerical model for incompressible flows and applies such a model for the first time to the simulation of atmospheric boundary layers capped by shallow cumulus and stratocumulus clouds. One needs to simulate a large domain, while locally having enough resolution to resolve the ...