An adaptive central‐upwind scheme on quadtree grids for variable density shallow water equations

Minimizing computational cost is one of the major challenges in modelling and numerical analysis hydrodynamics, ways to achieve this by use quadtree grids. In paper, we present an adaptive scheme on grids for variable density shallow water equations. A coupled system developed based work [M.A. Ghazizadeh, A. Mohammadian, Kurganov, Computers & Fluids, 208 (2020)]. The capable exactly preserving “lake-at-rest” steady states. continuous piecewise bi-linear interpolation bottom topography function used higher-order space order preserve positivity depth point values each cell. Necessary conditions are checked be able density, ensure achievement a stable scheme. At timestep, local gradients examined find new seeding points locally refine/coarsen grid.