可压缩纳维-斯托克斯方程ALE格式的熵稳定移动壁边界条件
Entropy-stable moving-wall boundary conditions for the ALE formulation of the compressible Navier-Stokes equations
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中文总结 AI 辅助
该研究针对移动域可压缩欧拉/纳维-斯托克斯方程，提出高阶熵稳定框架，结合SBP算子构造移动壁边界条件，经数值实验验证适用于复杂移动域多物理流问题。
中文摘要 AI 辅助
我们针对移动域上的可压缩欧拉方程和纳维-斯托克斯方程，提出了一种高阶熵稳定框架。描述域运动的时空映射被重构为任意拉格朗日-欧拉（ALE）格式，其中物理无粘通量与网格运动产生的贡献被统一处理。在连续层面，我们证明所提出的移动壁边界条件对欧拉方程是熵守恒的，对纳维-斯托克斯方程是熵稳定的；无滑移条件基于相对于移动壁的速度来表述，为熵平衡提供了有界的无粘贡献，而粘性项仅产生熵耗散。结合对角范数的熵稳定求和-非边界（SBP）算子与合适的数值通量，这些特性被扩展到半离散格式，从而在L²意义上实现非线性稳定性。通过大量数值实验验证了该方法的精度、鲁棒性和可扩展性，实验范围涵盖经典二维验证案例，以及涉及移动边界和流固耦合的大规模湍流与超声速模拟。结果证实，高阶熵稳定格式适用于广泛流态和多物理场应用中的复杂移动域问题。由于分析依赖于SBP特性而非特定离散化，该框架自然可扩展到基于对角范数SBP算子的广泛方法，包括有限体积法、有限元法和通量重构法。
英文摘要
We present a high-order entropy-stable framework for the compressible Euler and Navier-Stokes equations on moving domains. The space-time mapping describing the domain motion is recast in an arbitrary Lagrangian Eulerian (ALE) formulation, in which the physical inviscid fluxes and the contributions induced by mesh motion are treated in a unified manner. At the continuous level, we prove that the proposed moving-wall boundary conditions are entropy conservative for the Euler equations and entropy stable for the Navier-Stokes equations. The no-slip condition is formulated in terms of the velocity relative to the moving wall, yielding a bounded inviscid contribution to the entropy balance, while the viscous terms contribute only entropy dissipation. Using diagonal norm summation-by-parts (SBP) operators together with appropriate numerical fluxes, these properties are extended to the semi-discrete formulation, resulting in nonlinear stability in the $L^2$ sense. The accuracy, robustness, and scalability of the proposed method are demonstrated in practice through an extensive set of numerical experiments, ranging from canonical two-dimensional verification cases to large-scale turbulent and supersonic simulations involving moving boundaries and fluid-structure interaction. The results confirm the suitability of high-order entropy-stable schemes for complex moving-domain problems across a broad range of flow regimes and multiphysics applications. Because the analysis relies on the SBP property rather than on a particular discretization, the framework naturally extends to a broad class of methods based on diagonal-norm SBP operators, including finite volume, finite element, and flux reconstruction schemes.
