Staggered Scheme for Shallow Water Equations with Quadtree-subgrid

To get accurate results, high-resolution numerical simulations are often required. However, computation using high resolution grid often require larger computer memory and longer computational time. One way to overcome this problem is by adopting a scheme that can handle a non-homogeneous grid; i.e. a computational domain with two or more resolutions. In this work, a two-level quadtree-subgrid method was applied. It uses a combination of structured grid with hierarchical quadtree ordering. This method is applied on a staggered grid scheme for the two-dimensional shallow water equations. A benchmark simulation of wave run-up on a conical island was conducted for validation. Comparison between computing time of simulations using the fine grid and the quadtree-subgrid shows the effectiveness of this quadtree-subgrid scheme.