THE NUMERICAL-SOLUTION OF PARTIAL-DIFFERENTIAL EQUATIONS IN THE MODELING OF RIVER PROCESSES

Mathematical models of river processes result often in a system of partial differential equations (PDE's) of the form u(t) = F(t, x, u, u(x), u(xx)) with special initial and boundary conditions. In the general case of implicitly given boundary conditions the application of the method of lines yields to a system of differential-algebraic equations (DAE's). The DAE's are solved by Rosenbrock-Wanner methods (ROW) with step size control in time. After every time-step new discretisation points in space depending on the solution behaviour are selected. The application to a special variant of the Burgers equation and to a transport model in open channel flow is discussed.