A Fully Conservative Ghost Fluid Method & Stiff Detonation Waves

We present a new, fully conservative version of the ghost fluid method applicable for tracking material interfaces, inert shocks, and both deflagration and detonation waves in as many as three spatial dimensions. The exact discrete conservation properties are most important when tracking inert shocks and detonation waves, so that is the focus of this paper. In particular, we address the inviscid reactive Euler equations in the context of stiff detonation waves on coarse grids. The main difficulty here arises when the time scales of the chemical reaction are significantly shorter than the time scales of the fluid dynamics leading to a stiff source term and nonphysical wave phenomena. We use the level set method to track the location of the detonation wave and the ghost fluid method to treat the discontinuous quantities across the inert shock portion of that wave. This leads to a sharp non-smeared shock profile alleviating the nonphysical wave phenomena.