Depth-averaged Tidal Flow Simulation by Stabilized Finite Element Formulation in the Ocean Surrounding Indonesia

The final goal of this study is to predict marine environments in the ocean surrounding Indonesia by developing computational techniques based on computational fluid dynamics (CFD). As a preliminary step towards this goal, we have developed methodologies for simulating tidal flows in this paper. The mathematical model of tidal flows is based on depth-averaged 2D shallow water equations (SWEs). We use a stabilized finite element formulation with the Nitsche-type weak imposition of the slip boundary condition to discretize these equations. We propose new techniques to specify appropriate boundary conditions on curved coastlines and open boundaries. We apply harmonic analysis to compact all computational results. We also introduce a one-way nesting procedure to promote a higher accuracy and reflect larger scale effects in subsequent nested meshes. We have applied the present methodologies to a tidal flow simulation in the coastal area around the northern coast of Bali, Indonesia. In this area, we have been observing environmental factors and tidal current velocity in real time from September 2018. We compared the simulation results with the observation results, and discussed the prediction accuracies of the present methodologies.