Assessment of numerical issues in one-dimensional detonation wave representation

This thesis was an attempt to simulate the detonation waves and contact surfaces in unsteady flows with improved accuracy and efficiency through the use of adaptive mesh refinement (AMR). In the present work, the problem dealt with is the simulation of the working cycles of a pulsed detonation engine (PDE). A flexible code which can be used for any unsteady flow simulation was developed. The analysis was based on the quasi one-dimensional Euler equations and the reaction rate was modelled using a one-step irreversible reaction equation. The numerical simulations were carried out using two numerical schemes, namely. Roe's approximate Riemann solver and the advection upstream splitting method (AUSM).

Results of this numerical study show the importance and effects of increasing the spatial resolution. The use of adaptive mesh refinement made it possible to increase the spatial resolution with insignificant increases in cost of computations. The results also show that the contact surfaces cannot be captured accurately merely by increasing the spatial resolution, due to the high innate numerical diffusion of the flux schemes. The possibility of confining an interface to a few cell distances by adding a suitable confinement term has also been discussed.