适用于非理想状态方程的节点间断伽辽金方法：压力平衡保持与熵校正
Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction
AI总结：
本研究针对非理想状态方程，提出结合压力平衡保持、熵校正的间断伽辽金格式，分析了EPEC与APEC格式的特性，提升了流体模拟的鲁棒性。
AI中文摘要：
保结构间断伽辽金（DG）方法通常可提升真实流体高阶模拟的鲁棒性，除守恒性外，关键结构还包括压力平衡保持及至少满足一个熵不等式。本研究探讨采用严格压力平衡保持（EPEC）通量差分DG格式与近似压力平衡保持（APEC）通量差分DG格式的保守离散化，以及针对非理想状态方程（EOS）的低耗散校正实现的熵稳定格式。我们引入EPEC格式的分析，并基于Tadmor洗牌条件的推广提出此类通量的设计新流程；同时分析APEC DG格式，表明引入耗散界面罚项不会显著增大压力平衡误差，尤其在高阶近似下。最后，我们发现结合APEC通量差分格式时，熵校正可提升欠分辨解与长时间模拟的鲁棒性。
英文摘要：
Structure-preserving discontinuous Galerkin (DG) methods typically improve the robustness of high order simulations of real fluids. In addition to conservation, key structures include the preservation of pressure equilibrium and satisfaction of at least one entropy inequality. In this work, we investigate conservative discretizations using exactly pressure equilibrium conserving (EPEC) and approximately pressure equilibrium conserving (APEC) flux differencing DG formulations, as well as entropy stable formulations through the use of minimally dissipative corrections for non-ideal equations of state (EOS). We introduce an analysis of EPEC schemes and a new procedure for designing such fluxes based on a generalization of Tadmor's shuffle condition. We also analyze APEC DG schemes and show that the incorporation of dissipative interface penalization terms does not significantly increase pressure equilibrium errors, especially at higher orders of approximation. Finally, we observe that when combined with APEC flux differencing formulations, entropy correction improves robustness for under-resolved solutions and long-time simulations.
