Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations

One of the main challenges in computational simulations of gas detonation propagation is that negative density or negative pressure may emerge during the time evolution, which will cause blow-ups. Therefore, schemes with provable positivity-preserving of certain quantities such as density and pressure are desired. First order and second order positivity-preserving schemes were well studied, e.g., [10]. A simple solution for arbitrarily high order schemes was proposed recently in [22]. For high order discontinuous Galerkin (DG) method, even though the characteristicwise TVB limiter in [1, 2] can kill oscillations, it is not sufficient to maintain the positivity. In this paper, we first show an extension of the [22, 23, 24] to design positivity-preserving arbitrarily high order DG schemes for reactive Euler equations. Then we show a new simpler and more robust implementation of the positivity-preserving limiter than the one in [22]. Numerical tests show that the third order DG scheme with the new positivity-preserving limiter produces satisfying results even without the TVB limiter. AMS subject classification: 65M60, 76N15