标题： 熵守恒和熵稳定的电阻磁流体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，用于在绝热壁或指定热熵流的壁存在的情况下，为电阻磁流体力学方程施加非线性熵守恒和熵稳定的壁边界条件，涵盖了三种情况：电绝缘壁、有限电导率的薄壁以及完全导电壁。 该方法依赖于对角范数、求和-由部分和以及同时逼近项算子的形式主义和拟合性质。 通过线法，当所提出的边界条件数值施加方式与熵守恒或熵稳定的离散内部算子相结合时，整个区域可获得半离散的熵估计。 所得估计值模拟了连续水平上获得的整体熵估计。 使用罚流方法和同时逼近项技术弱化地施加壁上的边界数据，适用于守恒变量和熵变量的梯度。 高阶无结构网格上的间断谱配置算子（质量集中节点间断伽辽金算子）被用来展示新方法在弱施加边界条件方面的准确性、鲁棒性和有效性。 数值模拟验证了所提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-由部分和空间算子兼容，包括有限元、有限差分、有限体积、节点和模态间断伽辽金以及通量重建方案。 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.