Spline-based finite-element method for the stationary quasi-geostrophic equations on arbitrary shaped coastal boundaries

Abstract

Abstract This work concerns a B-spline based finite-element algorithm for the stationary quasi-geostrophic equations to treat the large scale wind-driven ocean circulation on arbitrary shaped domains. The algorithm models arbitrary shaped coastal boundaries on intra-element, or embedded boundaries. Dirichlet boundary conditions on the embedded boundaries are weakly imposed and stabilization is achieved via Nitsche’s method. We employ a hierarchical local refinement approach to improve the geometrical representation of curved boundaries. Results from several benchmark problems on rectangular and curved domains are provided to demonstrate the accuracy and robustness of the method. We also provide the Mediterranean sea example that illustrates the effectiveness of the approach in the wind-driven ocean circulation simulation.