A semi-group approach to the thin-film equation with general mobility

This thesis treats the thin-film equation which models the film height $h$ for a viscous film in the complete wetting regime. We show existence and uniqueness to the thin-film equation with mobility m(h) = hⁿ and mobility exponent n∈ (1,3/2)∪ (3/2,3). The thin-film equation is rewritten as an abstract Cauchy problem and usage of semi...

Verification, validation, and parameter study of a computational model for corrosion pit growth adopting the level-set method.: Part I: Corrosion

Corrosion is a phenomenon observed in structural components in corrosive environments such as pipelines, bridges, aircrafts, turbines, etc. The computational model of corrosion should enjoy two features: a) accurately considering the electrochemistry of corrosion and b) properly dealing with the moving interface between solid and electrolyte....

Verification, validation, and parameter study of a computational model for corrosion pit growth adopting the level-set method. Part II: Stress corrosion

Structural components in corrosive environments such as pipelines, bridges, aircrafts, and turbines are imposed to stress corrosion. A stress corrosion model for pit growth should a) accurately consider the electrochemistry of the corrosion process, b) properly deal with the moving interface between solid and electrolyte, and c) effectively...

Developing a second order accurate level-set method for solving the one-dimensional Stefan problem

This work aims at finding a second order accurate level-set method which solves the Stefan problem with non-homogeneous Dirichlet boundary conditions in one dimension. The numerical accuracy of the FTCS-scheme, BTCS-scheme and Crank-Nicolson scheme for the discretization of the heat equation was considered, as well as the accuracy of the first...

Simulation of drying and ?ooding in a tidal embayment using the level set method

A suite of sharp interface models for solid-state transformations in alloys

The work deals in particular with dissolution and growth of particles in solid-state alloys. Several models are presented and numerical solution procedures are summarized briefly. Further, some analytic solutions are considered shortly, which are useful to validate the numerical solutions. One model, which incorporates surface energy effects is...

A suite of sharp interface models for solid-state transformations in alloys

A suite of mathematical models for solid-state phase transformations in solid-state alloys is presented. The work deals in particular with dissolution and growth of particles in solid-state alloys. Several models are presented and numerical solution procedures are summarized briefly. Further, some analytic solutions are considered shortly, which...