发表机构
University of Stuttgart, Institute of Applied Analysis and Numerical Simulation, Chair of Applied Mathematics; Clausthal University of Technology, Institute of Mathematics, Numerical Analysis Research Group; Indian Institute of Technology Delhi, Department of Mathematics（斯图加特大学应用分析与数值模拟研究所应用数学教席; 克莱施塔尔工业大学数学研究所数值分析研究组; 德里印度理工学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为两层薄膜流双曲模型构造高阶熵耗散格式，比较精确与近似熵守恒通量，并在有限差分和谱元法中验证其性能与鲁棒性。
AI 中文摘要
本文针对描述不可混溶流体且含完全可溶溶质颗粒的两层薄膜流一阶动力学的双曲型守恒律系统，开发了高阶熵耗散格式。关键方面在于构造Tadmor意义下的熵守恒通量。在此，我们考虑并比较了两种不同的构造过程：精确公式化与通量评估中常用的简化近似。虽然近似方法在构造层面更简单且在实践中（也在其他情境中）经常使用，但其结构较弱，导致与精确公式化相比，在实现中增加了计算成本，而精确公式化的推导则复杂得多。我们将这些通量应用于熵耗散有限差分框架和熵耗散间断伽辽金谱元方法中。通过使用两种不同空间离散化的数值实验，我们研究了所提出方法的性能和鲁棒性，并证明了数值通量的选择对所得求解器的效率有显著影响。
英文摘要
In this article, we develop high-order, entropy-dissipative schemes for a hyperbolic system of conservation laws describing the first-order dynamics of two-layer thin-film flows of immiscible fluids with perfectly soluble solute particles. The key aspect is to construct entropy-conservative fluxes in the sense of Tadmor. Here, we consider and compare two different construction processes: an exact formulation and a commonly used simplified approximation in the flux evaluation. While the approximate approach is simpler at the level of construction and is frequently employed in practice (also in other contexts), it is less structured, leading to increased computational cost in the implementation compared to the exact formulation, which has been much more complicated to derive. We employ these fluxes within both an entropy-dissipative finite-difference framework and an entropy-dissipative discontinuous Galerkin spectral element method. Through numerical experiments using two distinct spatial discretizations, we investigate the performance and robustness of the proposed methods and demonstrate that the choice of numerical flux has a noticeable impact on the efficiency of the resulting solvers.
