Numerical simulations of shock waves reflection and interaction

The main objective of this dissertation is to detect and study the phenomena of reflection of one shock wave and interaction of two shock waves using numerical methods. In theory, solutions of non-linear Euler equations of compressive inviscid gas dynamics in two dimensions can display various features including shock waves and rarefaction waves. To capture the shock waves properly, highly accurate numerical schemes are designed according to second order Lax-Wendroff method. In this thesis, three numerical experiments were designed to show the reflection and interaction phenomena. Firstly, one shock was formed due to the encounter of two high speed gas flows, a reflected flow was formed due to the grid wall. It is clear to find the jump of the physical parameters, such as density, pressure, velocity (both in x and y directions) and energy, in the track of the incident shock wave and reflected shock wave. In the second experiment, two shock waves were formed symmetrically in a long and narrow area. Under the similar conditions with the previous experiment, these two shock waves intersect in the middle. Lastly, another interaction experiment was presented using different initial and boundary conditions. The experiment results of the last two experiments are similar: the change of various parameters getting drastic and chaotic in the interaction area (but still symmetric), while they are regular and clear in the outside of the interaction area. Conclusions and comparisons of the experiment results and its counterpart in theory were given in the end