AI 中文总结
本文针对可压缩流方程开发几何分裂IMEX框架，刚性区用隐式HDG法，非刚性区用显式DG法，研究两种隐式格式，通过界面条件和ARK格式实现时空耦合，经实验验证该方法能缓解刚性并加速，在时空上达高阶精度。
AI 中文摘要
在这项工作中，我们为可压缩流方程开发了一种几何分裂的隐式-显式（IMEX）框架，其中通过隐式可杂交间断伽辽金（HDG）方法处理刚性区域，而非刚性区域通过显式间断伽辽金（DG）方法处理。研究了两种隐式格式：混合HDG方法（HDG-MX）和原始内部罚函数HDG方法（HDG-IP）。通过适当的界面条件以保守方式实现隐式和显式解之间的空间耦合，同时通过使用加法龙格-库塔（ARK）格式保持时间同步。详细讨论了所得IMEX格式的计算性能。一系列数值实验的验证和确认表明，所提出的IMEX格式在空间和时间上均实现了高阶精度。性能研究进一步表明，该方法有效缓解了几何诱导的刚性，并且只要隐式区域选择得当，相对于完全显式的DG格式可提供高达约50倍的加速。
英文摘要
In this work, we develop a geometry-split implicit-explicit (IMEX) framework for the compressible flow equations, wherein stiff regions are treated via an implicit hybridizable discontinuous Galerkin (HDG) method, while non-stiff regions are treated via an explicit discontinuous Galerkin (DG) method. Two implicit formulations are investigated: a mixed HDG method (HDG-MX) and a primal interior-penalty HDG method (HDG-IP). The spatial coupling between the implicit and explicit solutions is achieved in a conservative manner by appropriate interface conditions, while the temporal synchronization is maintained through the use of additive Runge-Kutta (ARK) schemes. We provide a detailed discussion on the computational performance of the resulting IMEX schemes. Verification and validation over a range of numerical experiments confirm that the proposed IMEX schemes achieve high-order accuracy in both space and time. Performance studies further indicate that the approach effectively alleviates geometry-induced stiffness and can provide speedups of up to approximately 50 relative to a fully explicit DG scheme, provided that the implicit region is chosen appropriately.
