Numerical error control for second-order explicit TVD scheme with limiters in advection simulation

This paper analyzes the causes of the numerical errors in terms of numerical diffusion and compression arising from the use of explicit second-order total variation diminishing (TVD) schemes in one-dimensional advection simulation. It demonstrates that different TVD limiters may have very different performances in different advection simulations, because of the so-called numerical diffusion and compression. The accuracy of the computed results is found to depend on not only the limiter functions themselves but also the advection features such as the concentration distribution, advection velocity and time step, etc. According to such relations, the effective ranges of the MIN_MOD, Van Leer and SUPERBEE limiters are characterized by introducing a dimensionless parameter which reflects the key features of advections, aiming to provide an approach to select a proper TVD limiter in advection simulation.