发表机构
McGill University（麦吉尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种同时满足熵守恒与动能保持的两点通量，通过推广Ranocha方法至多组分，解决了现有通量不能兼得两种性质的问题，适用于多组分可压缩流动模拟。
AI 中文摘要
在过去十年中，高阶熵稳定（ES）方法引起了计算流体力学（CFD）研究界的广泛兴趣，因为我们寻求以高精度和鲁棒性模拟实际工程应用。随着工业界进一步深入超音速飞行和太空旅行，我们需要能够模拟流体中多种化学组分相互作用和混合的流动的方案。因此，目前有相当多的努力集中在为多组分（MS）流动开发高阶ES格式。这些熵稳定格式的一个关键要素是两点通量，它决定了所得高阶离散化的性质。因此，只有当两点通量也反映这些性质时，数值格式才能拥有诸如熵守恒和动能保持等重要性质。目前，文献中用于高阶ES多组分求解器的两点通量不保持动能（KEP）。在这篇短通讯中，我们通过将Ranocha的单组分方法推广到多组分，开发了一种既熵守恒（EC）又动能保持的两点通量。新提出的EC和KEP通量使用密度脉冲平流和泰勒-格林涡案例与文献中现有的两点通量进行了测试。结果表明，EC和KEP通量同时保留了这两种性质，而其他通量仅保留了所需性质中的一种。由于两点通量决定了所得格式的性质，所提出的通量是模拟多组分可压缩流动的理想选择。
英文摘要
High-order entropy stable (ES) methods have attracted much interest in the computational fluid dynamics (CFD) research community over the past decade, as we seek to simulate practical engineering applications with high accuracy and robustness. As industry delves further into supersonic flight and space travel, we need schemes capable of modelling flows with multiple chemical species that interact and mix within the fluid. As such, there is a considerable amount of effort currently being focused on developing high-order ES schemes for multi-species (MS) flow. A key ingredient for these entropy stable schemes is the two-point flux, which determines the properties of the resulting high-order discretization. As such, the numerical scheme can possess important properties such as entropy conservation and kinetic energy preservation only if the two-point flux also mirrors these properties. At present, in the literature, the two-point fluxes used for high-order ES multi-species solvers are not kinetic energy preserving (KEP). In this short communication we develop a two-point flux that is both entropy conserving (EC) and kinetic energy preserving by adapting Ranocha's single-species methodology for multi-species. The newly proposed EC and KEP flux is tested against existing two-point fluxes in the literature using the density pulse advection and Taylor-Green vortex cases. It is shown that EC and KEP flux retains both properties while the other fluxes only retain one of the desired properties. Since the two-point flux dictates the properties of the resulting scheme, the proposed flux is the ideal option for simulating multi-species compressible flow.
