ON OPEN BOUNDARIES IN THE FINITE-ELEMENT APPROXIMATION OF 2-DIMENSIONAL ADVECTION-DIFFUSION FLOWS

A steady-state and transient finite element model has been developed t o approximate, with simple triangular elements, the two-dimensional ad vection-diffusion equation for practical river surface flow Simulation s. Essentially, the space-time Crank-Nicolson-Galerkin formulation sch eme was used to serve for a given conservative how-held. Several kinds of point sources and boundary conditions, namely Cauchy and Open,;; w ere theoretically and numerically analysed. Steady-state and transient numerical tests investigated the accuracy of boundary conditions on i nflow, noflow and outflow boundaries where diffusion is important (dif fusive boundaries). With the proper choice of boundary conditions, the steady-state Galerkin and the transient Crank-Nicolson-Galerkin finit e element schemes gave stable and precise results for advection-domina ted transport problems. Comparisons indicated that the present approac h can give equivalent or more precise results than other streamline up wind and high-order time-stepping schemes. Diffusive boundaries can be treated with Cauchy conditions when the flow enters the domain (inflo w), and with Open conditions when the flow leaves the domain (outflow) , or when it is parallel to the boundary (noflow). Although systems wi th mainly diffusive noflow boundaries may still be solved precisely wi th Open conditions, they are more susceptible to be influenced by othe r numerical sources of error. Moreover, the treatment of open boundari es greatly increases the possibilities of correctly modelling restrict ed domains of actual and numerical interest. (C) 1997 by John Wiley & Sons, Ltd.