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Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. (English) Zbl 1243.80011
In this paper it is provided an extension of the positivity-preserving techniques to construct robust high order Runge-Kutta discontinuous Galerkin schemes for reactive Euler equations modeling gaseous detonations. The numerical tests developed in the paper under review suggest that the positivity-preserving limiter is sufficient to stabilize the high order discontinuous Galerkin method without the TVB limiter. At the same time, robust high order Runge-Kutta discontinuous Galerkin schemes can successfully simulate detonation diffraction cases in which the density or pressure of the numerical solution may become negative without the positivity-preserving limiter.

MSC:
80A25 Combustion
76J20 Supersonic flows
80A32 Chemically reacting flows
35Q31 Euler equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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