A new numerical approach for the advective‐diffusive transport equation

A new numerical solution procedure is presented for the one‐dimensional, transient advective‐diffusive transport equation. The new method applies Herrera's algebraic theory of numerical methods to the spatial derivatives to produce a semi‐discrete approximation. The semi‐discrete system is then solved by standard time marching algorithms. The algebraic theory, which involves careful choice of test functions in a weak form statement of the problem, leads to a numerical approximation that inherently accommodates different degrees of advection domination. Algorithms are presented that provide either nodal values of the unknown function or nodal values of both the function and its spatial derivative. Numerical solution of several test problems demonstrates the behavior of the method.