2025 Volume 81 Issue 16 Article ID: 24-16200
High-resolution Shallow Water simulations have the issues of its computational cost and numerical instability due to the steep gradient of water surface. For these issues, hp-adaptive Discontinuous Galerkin (DG) Method has been proposed to control the grid resolution and the order of elements. However, the adequate adaptive strategies haven’t been well developed for shallow water problems, to decide how to control the grid resolution and order of accuracy against numerical oscillations especially for structured/unstructured mixed grids. In this study, we proposed a new adaptive strategy which combines the indicators of the cell average gradient and smoothness of the solution on the Systematic Grid which realizes the analysis on arbitrary grid. We applied the present adaptive strategy and the mixed grids to oblique hydraulic jump and equatorial Rossby modon problems. We confirmed from the numerical experiments that the proposed adaptive strategy effectively suppressed the numerical oscillation while keeping mass conservation and lead to efficient and accurate analysis on the mixed grid.
