In production processes of micro-electronics, optical and mechanical coatings and solar cells, high-purity materials in the form of a powder or a thin film are significant importance. The deposition of thin films on irregularly shaped surfaces can be done by chemical vapor deposition (CVD). Computer simulations are widely used to design CVD reactors and to optimize the process itself. The core of a computer simulation is a mathematical model of the gasflow and all chemical processes within the CVD reactor. A lot of (commercial) computer software has been written for CVD simulation. The emphasis has always been on modeling and validation. For the 'old' CVD processes this approach was sufficient. However, with the deposited films getting thinner and thinner, process times are reduced and transient times become more important. Further, the technology is moving towards inherent transient CVD processes (such as atomic layer deposition) making instationary simulations indispensable. Computing the time-dependent solution of the underlying mathematical equations is hard, because the involved chemistry makes these equations hard to solve. Commercial CFD software packages have often great problems to compute these solutions. Solutions computed by various codes have been reported to differ a lot and the computational times needed to find solutions are generally excessive. In this thesis a rigorous mathematical approach has been applied to these problems, with the aim to reduce computational times for simulations of CVD and related applications. The numerical techniques proposed in this thesis enables us to perform instationary, multi-dimensional gas flow simulations with multi-species, multi-reaction CVD chemistry in a computationally efficient way.