We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

翻译：我们提出了一种新的Nitsche型方法，用于在弯曲边界上使用高阶有限元对可压缩冲击流体动力学方程进行拉格朗日离散化时，弱强制执行法向速度边界条件。具体而言，变分公式被适当修改以强制执行自由滑移壁面边界条件，同时不扰动用于表示解的函数空间结构，与传统方法相比实现了显著简化。总能量得以守恒，所得质量矩阵在时间上保持恒定。通过涉及非平凡弯曲边界的大量测试，验证了所提方法的鲁棒性和准确性。