Finite Element Characteristic Advection Model

Abstract

For advection‐dominated transport processes, the traditional numerical techniques for solving the advection‐diffusion equation fail because of numerical oscillations. Fractional step solutions, in which the advection and diffusion processes are treated in separate steps, have been proposed as one way of overcoming this problem. Here a solution to the advection step based on the method of characteristics on a fixed grid is used. Interpolation is achieved with the finite element technique. Linear and quadratic elements are evaluated in terms of artificial diffusion, phase, and other errors. It was found that linear interpolation creates too much numerical diffusion, while the quadratic scheme is reasonably accurate, but under certain conditions generates spurious extrema. A method retaining the accuracy of the quadratic interpolation and eliminating its shortcoming is suggested. Boundary conditions and source loadings are considered in detail. An application of the model to salinity distribution resulting from canal discharges in Biscayne Bay is described.