In this work, models for simulating reactive supersonic flows were developed and implemented. On one hand, experiments in shock tubes were simulated to investigate ignition phenomena and boundary layer effects. On the other hand, simulations of detonation waves were conducted to analyze properties related to cell structure and cell stabilization.

For the simulation of compressible flows, the in-house code PsiPhi was first expanded. Approximate Riemann solvers and characteristic boundary conditions were used. Due to the dissipative nature of Up- wind methods, interpolation methods of higher accuracy were also tested and applied to adequately rep- resent turbulent flows. For simulating ignition processes, a finite-rate chemistry combustion model was employed, which is computationally more intensive compared to tabulated combustion models. There- fore, implicit and semi-implicit solvers for systems of ordinary differential equations were implemented to enhance computational efficiency. The integration of an Operator-Splitting framework further led to a reduction in computational costs.

Subsequently, a workflow was developed for simulating shock tube experiments, where only a small portion of the shock tube needs to be computed, but with high spatial resolution. Initially, a smaller auxiliary calculation was needed to simulate the initial Riemann problem at the start of the experiment. After the incident shock wave has fully developed, a predefined region around the incident shock wave is saved and used as the initial solution in the subsequent main simulation, which covers only the end part of the shock tube. Due to the formation of a boundary layer behind the incident shock, the state variables at the inlet boundary of the computational domain change. Therefore, a boundary condition was developed, which combines models for laminar boundary layers, turbulent boundary layers, boundary layer transition, and their influence on the core flow based on the “Small Perturbation Theory”, specifying the variables as a function of wall distance and time. This approach was validated using experimental data and was able to reproduce experiments where an unintended ignition occurred far from the end wall. Additionally, one of the first 3D simulations of shock tube experiments was able to demonstrate ignition caused by reflected shock bifurcation.

In the second part of this work, the propagation of detonation waves in channels and tubes was in- vestigated. To allow for high numerical resolution, a relative coordinate system was used, ensuring that the averaged detonation front is stationary and can be numerically examined with a small computational domain. The results were compared with experimental data using numerical soot foils. The average cell width and size distribution could be satisfactorily reproduced. This has been achieved by only a few stud- ies so far, as often heavily simplified one-step reaction mechanisms were used due to cost considerations. The data also served as a basis to develop a geometrically efficient model for the detonation cell struc- ture. A stability hypothesis for detonation cell sizes was also verified based on temporally highly resolved results and was confirmed for the mixtures investigated here.