The method of lines and the advective equation

Abstract

The linear advective equation is simple in form and yet it is one of the most difficult equations to solve accurately by numerical means. Because its be havior is similar to that of the conservation equa tions of compressible one- or two-phase flow, the advective equation is extremely useful for testing numerical schemes. This paper summarizes techniques for solving the ad vective equation using, the method of lines on a digi tal or hybrid computer, and assesses how suitable they are for incorporation into large simulations. Some of the dangers of using artificial dissipation terms are described, and a weighted-residual tech nique is shown to be very effective.