Enhancing the Capture of Two-dimensional, Shock-Induced Detonation Fronts using Harten’s Artificial Compression Method on Underresolved Cartesian Grids

Abstract

In the problems of detonation we are going to present here, the capture of shocks is crucial, since from its accuracy depends the very physical relevance of the whole solution. We already obtained some improvements in the capture of detonation fronts on underresolved grids in the one-dimensional case thanks to Harten's artificial compression [1], [2], and we now turn to two-dimensional cartesian grids. In two space dimensions, the complexity of the discontinuity implies not only the location and speed of the front, but also its shape. These three aspects will be explored here, for the ZND detonation model, based on Euler's system. We will use two-dimensional central schemes for main computations, namely the classical "Lax-Friedrichs" first order scheme and the second order "Jiang-Tadmor" scheme [3]. To each of these methods, we will add two different versions of ACM (Artificial Compression Method), one that uses space splitting, and the other based on directional differencing [4]. Finally, as ACM require a good knowledge of the regions of the solution potentially carrying discontinuities, it will be assisted by a DoD (Detector of Discontinuities) based on the entropy production rate.