标题： 熵守恒和熵稳定的电阻磁流体动力学方程的固体壁边界条件 显示英文标题

标题： Entropy conservative and entropy stable solid wall boundary conditions for the resistive magnetohydrodynamic equations

摘要： 我们提出了一种新颖的技术，用于在存在绝热壁或具有预定热熵流的壁的情况下，对电阻磁流体动力学方程施加非线性熵守恒和熵稳定的壁边界条件，解决了三种情况：电绝缘壁、有限电导率的薄壁以及完美导电壁。 该方法依赖于对角范数、求和-分部和同时逼近项算子的形式和仿射性质。 使用线法，当所提出的边界条件数值施加与熵守恒或熵稳定的离散内部算子耦合时，可以获得整个区域的半离散熵估计。 所得估计模仿了在连续水平上获得的全局熵估计。 使用惩罚通量方法和同时逼近项技术，对保守变量和熵变量的梯度，在壁面上弱施加边界数据。 使用高阶非结构化网格上的不连续谱插值算子（质量集中节点不连续伽辽金算子）来展示新过程的准确性、鲁棒性和有效性，以弱强制边界条件。 数值模拟证实了所提出技术的非线性稳定性，并应用于三维流动。 所描述的过程与任何对角范数求和-分部空间算子兼容，包括有限元、有限差分、有限体积、节点和模态不连续伽辽金以及通量重构方案。 显示英文摘要

摘要： We present a novel technique for imposing non-linear entropy conservative and entropy stable wall boundary conditions for the resistive magnetohydrodynamic equations in the presence of an adiabatic wall or a wall with a prescribed heat entropy flow, addressing three scenarios: electrically insulating walls, thin walls with finite conductivity, and perfectly conducting walls. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts, and simultaneous-approximation-term operators. Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions is coupled with an entropy-conservative or entropy-stable discrete interior operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation operators (mass lumped nodal discontinuous Galerkin operators) on high-order unstructured grids are used to demonstrate the new procedure's accuracy, robustness, and efficacy for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional flows. The procedure described is compatible with any diagonal-norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, nodal and modal discontinuous Galerkin, and flux reconstruction schemes.