We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier-Stokes and Darcy problem. We show existence and uniqueness of a solution and present an optimal a priori error analysis for the fully discrete problem when using Backward Euler time stepping. The theoretical results are verified by numerical examples.

翻译：我们提出了一种用于耦合瞬态Navier-Stokes与Darcy问题的强守恒且压力鲁棒的混合化间断Galerkin方法。我们证明了解的存在唯一性，并给出了采用向后欧拉时间步进的全离散问题的最优先验误差分析。数值算例验证了理论结果。