2019/11/27 by Mohammad A. Ghazizadeh, Ghazizadeh, Mohammad A., Abdolmajid Mohammadian +3
Earth and Planetary Sciences · Engineering · #Meteorological Phenomena and Simulations #Computational Fluid Dynamics and Aerodynamics #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.1911.12002
We present an adaptive well-balanced positivity preserving central-upwind\nscheme on quadtree grids for shallow water equations. The use of quadtree grids\nresults in a robust, efficient and highly accurate numerical method. The\nquadtree model is developed based on the well-balanced positivity preserving\ncentral-upwind scheme proposed in [A. Kurganov and G. Petrova, Commun. Math.\nSci., 5 (2007), pp. 133--160]. The designed scheme is well-balanced in the\nsense that it is capable of exactly preserving "lake-at-rest" steady states. In\norder to achieve this as well as to preserve positivity of water depth, a\ncontinuous piecewise bilinear interpolation of the bottom topography function\nis utilized. This makes the proposed scheme capable of modelling flows over\ndiscontinuous bottom topography. Local gradients are examined to determine new\nseeding points in grid refinement for the next timestep. Numerical examples\ndemonstrate the promising performance of the central-upwind quadtree scheme.\n