Adaptivity is crucial for addressing practical challenges of the next decades. In this regard, recent surveys [117] highlight that it continues to be a major bottleneck in computational fluid dynamics workflow. We introduce mixed non-conforming discontinuous Galerkin discretization for the full Boltzmann equation in 2D/3D. These schemes have been designed for efficiency — motivated in part by spectral and isogeometric weighted collocation methods — and retain an optimal $O(p+1)$ convergence for a p order approximation for non-linear kinetic systems on non-orthogonal grids. In this setting, it is possible to analyze highly complex problems of industrial strength i.e., structured, unstructured, mixed, irregular, multi-domain (multi-block) adaptive geometries at massively parallel scale (ten thousand cores or beyond). Mixed domains permit flexible mesh generation, whereas local nature of discontinuous Galerkin permits construction of adaptive numerical schemes that scale well. To address flows in mixing regime (low/high rarefaction), we couple the scheme with an asymptotic preserving implicit-explicit time discretization. These schemes are iteration free and applicable for a wide range of rarefied flows from free-molecular to continuum. To ensure stability in presence of shocks, we describe a method of constructing limiters on non-conforming grids. Finally, we show that the computational overhead for solving kinetic equations on non-conforming structured/unstructured domains is negligible relative to conforming domains. So, there is no reason to not prefer non-conforming unstructured domains.

适应性对于解决未来几十年的实际挑战至关重要。在这方面，最近的调查 [117] 强调它仍然是计算流体动力学工作流程中的主要瓶颈。我们为 2D/3D 中的完整 Boltzmann 方程引入了混合非一致性不连续 Galerkin 离散化。这些方案是为提高效率而设计的——部分原因是光谱和等几何加权搭配方法——并保持最佳$哦(磷+1)$非正交非线性动力学系统的p级近似收敛网格。在这种情况下，可以分析具有工业强度的高度复杂的问题，即结构化、非结构化、混合、不规则、多域（多块）自适应几何在大规模并行规模（一万个核心或更多）。混合域允许灵活的网格生成，而不连续 Galerkin 的局部性质允许构建缩放良好的自适应数值方案。为了解决混合状态下的流动（低/高稀疏），我们将该方案与渐进保持隐式显式时间离散化相结合。这些方案是无迭代的，适用于从自由分子到连续体的各种稀薄流动。为确保存在冲击时的稳定性，我们描述了一种在不合格网格上构建限制器的方法。最后，我们表明，相对于一致域，求解非一致结构/非结构域上的动力学方程的计算开销可以忽略不计。因此，没有理由不喜欢不符合规范的非结构化域。