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In this second part of our two-part paper, we extend to multiple spatialdimensions the one-dimensional, fully conservative, positivity-preserving, andentropy-bounded discontinuous Galerkin scheme developed in the first part forthe chemically reacting Euler equations. Our primary objective is to enablerobust and accurate solutions to complex reacting-flow problems using thehigh-order discontinuous Galerkin method without requiring extremely highresolution. Variable thermodynamics and detailed chemistry are considered. Ourmultidimensional framework can be regarded as a further generalization ofsimilar positivity-preserving and/or entropy-bounded discontinuous Galerkinschemes in the literature. In particular, the proposed formulation iscompatible with curved elements of arbitrary shape, a variety of numerical fluxfunctions, general quadrature rules with positive weights, and mixtures ofthermally perfect gases. Preservation of pressure equilibrium between adjacentelements, especially crucial in simulations of multicomponent flows, isdiscussed. Complex detonation waves in two and three dimensions are accuratelycomputed using high-order polynomials. Enforcement of an entropy bound, asopposed to solely the positivity property, is found to significantly improvestability. Mass, total energy, and atomic elements are shown to be discretelyconserved.

Positivity-preserving and entropy-bounded discontinuous Galerkin method  for the chemically reacting, compressible Euler equations. Part II: The  multidimensional case