This work started with the attend to develop a new kind of simulation tool avoiding general well known problems concerning local oxidation. A particle dynamic algorithm based on cellular automata [Zan93] should be used to solve the problem of local oxidation instead of applying standard numeric methods such as finite elements or finite boxes. Since first attempts on this area concerning diffusion processes have been very promising [Rad94] further investigations seemed to be justified.
The big difference between diffusion and local oxidation is the type of differential equation that describes the physical phenomena of both effects. In case of diffusion the differential equation can be classified as a parabolic type and, we have, among others, an elliptic type for oxidation. In other words, whereas the parabolic differential equation implicitly acts like a cellular automata, which means, that a local change in concentration can just be realized in the very near neighborhood and does not effect any other areas, oxidation causes an immediate effect across the whole simulation domain in case of stress changes. Since the temporal distribution of shock-waves (which for instance implies a local physical law that can be handled by cellular automata) is not of primary interest for oxidation simulations the dissemination of mechanical stresses has to be accelerated to get a fast steady state solution. Therefore, a hierarchical cellular automata has been developed, where in upper regions (big cells) low frequent solutions and in lower regions (small cells) high frequent ones are smoothed - similar to a multi-grid solver [Jop93]. Although first success was in sight it turned out that it is hardly possible to fulfill all requirements on a professional simulation tool using cellular automata techniques. The most striking points are:
All these arising problems using a cellular automata let us come to the decision that a well established technique, such as a simulator based on finite elements, finite boxes or finite differences, would be more satisfying than using a new methodology that lacks of physical descriptions as well as real progress in comparison to standard discretization methods. Therefore AMIGOS has been developed which offers the possibility for rapid prototyping of several physical problems. Although this thesis was devoted to the simulation of oxidation processes in three dimensions, several other models, such as pair-diffusion, thermodynamic processes, segregation and grid adaptation are also presented to show the flexibility of the developed simulation system.
The thesis is organized as follows: In Chapter 2 a short description of the physical basics of diffusion and oxidation is presented. Chapter 3 provides an introduction into general numerical discretization methods, such as finite elements and finite boxes with the intend to introduce the mathematical basics that are necessary to understand the rapid prototyping abilities of AMIGOS. In Chapter 4 a detailed description about the implementation and features of AMIGOS is given, where the possibilities of AMIGOS are presented with the help of several examples. Chapter 5 provides a detailed description of modeling local oxidation, especially the mechanical behavior of the material. Furthermore, a new model is presented that combines diffusion, chemical reaction and mechanical deformation in a single coupled numerical model that is used to solve several examples of typical oxidation processes. The thesis concludes with a brief discussion of the achieved results and gives some outlook for future work.