Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. In this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

熵稳定方案确保物理上有意义的数值解在适当的边界条件下也满足半离散熵不等式。在这项工作中，我们描述了可压缩 Navier-Stokes 方程中粘性项的离散化，它能够为不连续的伽辽金 (DG) 离散化简单而明确地施加熵稳定的无滑移和反射（对称）壁边界条件。具体来说，我们推导出了为模态熵稳定 DG 公式施加绝热无滑移和反射（对称）边界条件的方法，该公式保持半离散熵不等式。数值结果证实了所提出方法的鲁棒性和准确性。