Application of Positivity-Preserving Discontinuous Galerkin Scheme in Gaseous Detonations

In numerical simulation of gaseous detonation, due to the complexity of the computational domain, negative density and pressure often emerge in high resolution numerical computing, which leads to blow-ups. The paper provides high order discontinuous Galerkin (DG) positivity-preserving scheme for two-dimensional (2D) Euler equations with two-step chemical reaction which preserve positivity of density, pressure and chemical reaction process. A positivity-preserving limiter is added in high order DG scheme without influencing conservation, accuracy and stability. The method is verified by parallel numerical simulations and is approved to be well applied to numerical simulation of gaseous detonation propagation with complicated geometry boundary.