Second Order Positive Schemes by means of Flux Limiters for the Advection Equation.

In this paper, we study first and second order positive numerical methods for the advection equation. In particular, we consider the direct discretization of the model problem and comment on its superiority to the so called method of lines. Moreover, we investigate the accuracy, stability and positivity properties of the direct discretization. The numerical results related to several test problems are reported. [ABSTRACT FROM AUTHOR]