AI 中文总结
本文提出一种新的高阶熵稳定等温无滑移壁面边界条件，基于SBP-SAT算子，确保离散熵不等式，并在标准基准问题上验证其结构保持与设计阶精度。
AI 中文摘要
熵稳定边界条件对于确保相应数值格式满足离散熵不等式至关重要，从而在离散层面模拟可压缩Navier-Stokes方程的热力学第二定律。Parsani 2014年（引用\cite{parsani2014entropy}）提出了可证明熵稳定的绝热壁面边界条件。Dalcin 2019年（引用\cite{dalcin2019conservative}）进一步将这些离散壁面边界条件推广到移动绝热固体壁面或具有规定热通量的壁面，适用于使用求和-分部（SBP）和同时逼近项（SAT）算子离散的可压缩Navier-Stokes方程。目前文献中尚无使用SBP-SAT算子的等温壁面边界条件的熵稳定格式。本文提出了一种新的等温无滑移壁面边界条件，其能够：1）以设计阶精度强制执行$T|_{y=0}=T^{wall}$和$\vec{v}|_{y=0}=\vec{v}^{wall}$条件，同时保持稳定性；2）在壁面处提供正确的熵产生符号；3）在离散层面模拟Navier-Stokes方程的熵平衡。所提出方法的结构保持和设计阶特性已在可压缩流动的标准基准问题上得到验证和确认。
英文摘要
Entropy stable boundary conditions are critical for ensuring that the corresponding numerical scheme satisfies the discrete entropy inequality, thus, mimicking the second law of thermodynamics for the compressible Navier-Stokes equations discretely. Provably entropy-stable adiabatic wall boundary conditions were introduced in Parsani 2014~\cite{parsani2014entropy}. These discrete wall boundary conditions were further generalized in Dalcin 2019~\cite{dalcin2019conservative} to a moving adiabatic solid wall or a wall with a prescribed heat flux for the compressible Navier--Stokes equations discretized by using summation-by-parts (SBP) and simultaneous-approximation-term (SAT) operators. Currently no entropy-stable formulation using SBP-SAT operators for isothermal wall boundary conditions is available in the literature. This paper presents a new isothermal no-slip wall boundary conditions that: 1) enforces the $T|_{y=0}=T^{wall}$ and $\vec{v}|_{y=0}=\vec{v}^{wall}$ conditions with the design order of accuracy while maintaining stability, 2) provides the correct sign of entropy production at the wall, and 3) mimics the entropy balance of the Navier-Stokes equations at the discrete level. The structure-preserving and design-order properties of the proposed methodology are demonstrated and verified on standard benchmark problems for compressible flows.
