NEW COLLOCATION METHOD FOR THE SOLUTION OF THE CONVECTION-DOMINATED TRANSPORT-EQUATION

A modified Hermitian basis function is developed as a means of enhancing numerical solutions to the convection‐dominated transport equation using orthogonal collocation. An asymmetric approximation to the first‐order spatial derivative is provided so that oscillations in the numerical solution are eliminated while introducing a minimum amount of numerical dispersion. The degree of assymetry in the basis function required to achieve a smooth solution is shown to be dependent upon the magnitude of the convective and dispersive terms. Copyright 1979 by the American Geophysical Union.