Adaptive grid shallow water modeling Original Research Article

Adaptive grid generation procedure is coupled with the solver of the shallow water equations. The theory of harmonic maps is used as a theoretical framework for grid generation. The problem of constructing harmonic coordinates on the surface of the graph of control function is formulated. The projection of these coordinates onto a physical region produces an adaptive-harmonic grid. Modification of the finite element method, similar to the upwind differencing is used for solving the shallow water equations. All algorithms are described in detail. Results of computations for the Azov Sea are presented.