Using of FEM for Modeling of Compatible Movement of Surface Kinematic Waves and River Flows

The mathematical model of unsteady fluid flow in the open pseudoprizmatic channel was considered. It was derived from the general Navier-Stokes equations. For this model formulated stability criterion of flow which depends on the emergence of waves with increasing amplitude. Variational formulation of the problem was built and solved by finite element method. The influence of the order approximations and selecting basic functions for convergence to a solution of the problem was analyzed. Investigated the movement of water in the river network, where the network branches are united and form a tree structure of river basin, where in each section of the channel can be changed its trajectory and angle of the midline of bottom. Results approved on test examples with complex relief of bottom and it shows the influence of the choice of basis functions on accuracy of the solutions and calculated orders of convergence for time and spatial variables.