In this second part of our two-part paper, we extend to multiple spatial dimensions the one-dimensional, fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme developed in the first part for the chemically reacting Euler equations. Our primary objective is to enable robust and accurate solutions to complex reacting-flow problems using the high-order discontinuous Galerkin method without requiring extremely high resolution. Variable thermodynamics and detailed chemistry are considered. Our multidimensional framework can be regarded as a further generalization of similar positivity-preserving and/or entropy-bounded discontinuous Galerkin schemes in the literature. In particular, the proposed formulation is compatible with curved elements of arbitrary shape, a variety of numerical flux functions, general quadrature rules with positive weights, and mixtures of thermally perfect gases. Preservation of pressure equilibrium between adjacent elements, especially crucial in simulations of multicomponent flows, is discussed. Complex detonation waves in two and three dimensions are accurately computed using high-order polynomials. Enforcement of an entropy bound, as opposed to solely the positivity property, is found to significantly improve stability. Mass, total energy, and atomic elements are shown to be discretely conserved.

翻译：在本两篇系列论文的第二部分中，我们将第一部分为化学反应欧拉方程开发的一维全守恒、可保持正性且熵有界的不连续伽辽金格式推广至多维空间。我们的主要目标是利用高阶不连续伽辽金方法在不要求极高分辨率的情况下实现复杂反应流动问题的鲁棒精确解。研究考虑了变热力学性质与详细化学反应机制。我们的多维框架可视为对文献中类似可保持正性和/或熵有界不连续伽辽金格式的进一步推广。具体而言，所提出的公式与任意形状的曲边单元、多种数值通量函数、具有正权重的通用求积规则以及热完全气体混合物兼容。论文讨论了相邻单元间压力平衡的保持问题——这在多组分流动模拟中尤为关键。通过使用高阶多项式，我们精确计算了二维和三维的复杂爆轰波。研究发现，相较于仅保持正性性质，强制执行熵界可显著提升稳定性。质量、总能量和原子元素均被证明具有离散守恒性。