Impact of Limiters on Accuracy of High-Resolution Flow and Transport Models

Abstract

High-resolution finite volume schemes used to predict mass transport and free surface flows utilize limiters such as Minmod, Double Minmod, and Superbee to prevent spurious oscillations commonly associated with second-order accurate schemes. These limiters effectively switch between the classical Lax-Wendroff, Warming-Beam, and Fromm schemes, or amplified versions of these schemes that artificially increase gradient magnitudes to minimize damping of high frequency solution components. A Von Neumann analysis illustrates that gradient or slope amplification reduces numerical dissipation, but also increases the phase error and should therefore be cautiously used. The Double Minmod limiter closely mimics the Fromm scheme and possesses better phase accuracy than the Minmod and Superbee limiters. Near sharp solution gradients, slope amplification used by the Double Minmod and Superbee limiters reduces artificial smearing. The Minmod limiter does not use slope amplification and therefore yields the most solution smearing. Results of model tests show that the combined attributes of the Double Minmod limiter yield more accurate predictions of mass transport and circulation zones in shallow water than those of other limiters such as Minmod and Superbee.