FESW - - a finite-element Fortran IV program for solving the shallow-water equations

A Fortran IV computer program is documented, implementing a Galerkin finite-element method for solving the non-linear shallow-water equations on a limited domain. The resulting ordinary differential equations are integrated using a finite-difference discretization method in time. A time-extrapolated Crank-Nicolson numerical integration scheme is employed to quasi-linearize the non-linear advective terms. The three equations constituting the shallowwater equations are coupled at each time step, making it possible to use larger time steps. The output of the program includes a line printer plot contouring the height field. A compact storage scheme is provided in which advantage has been taken of the sparsity of the global matrices. A Gauss-Seidel iterative procedure is employed to solve the liaear systems of algebraic equations at each time step. Program options include the determination at each time step of the numerical integration of two of the integral invariants of the shallow-water equations. Stable long-term runs were achieved using a 30minute time step.