Investigation of Geoinformation Models of Water Flows in Pseudoprismatic Channels

A mathematical model describing the motion of water in pseudoprismatic channels with uneven bottom is constructed. The shape of the cross-section of the channel may be asymmetric, so the banks of the channel are described using known functions, or their approximations. For this model, initial-boundary and variational problems are formulated. The scheme of regularization of equations is constructed, which allows it to be used both for flat surfaces of the bottom of the channel, and for those in which the gradient of the slope changes rapidly. The variation problem is solved by the finite element method. Discretization by spatial variables was carried out by dividing the region into triangular finite elements using bilinear basis functions; time discretization was carried out using a one-time recurrent circuit. The model is tested in various test cases. In order to implement the constructed models an application software that allows using algorithms of constructed projection schemes for real territories was developed.