On Enhancing the Dissipative Behavior of Active Flux Advection Schemes

TL;DR

This paper improves the dissipative properties of the third-order Active Flux advection scheme by reformulating it and adding parameters, with validation through numerical experiments.

Contribution

It introduces modifications and additional parameters to enhance the dissipative behavior of the Active Flux scheme, which is a novel approach.

Findings

Modified scheme shows improved dissipation in numerical tests.

Parameter effects on scheme performance are systematically studied.

Numerical experiments validate the enhanced dissipative properties.

Abstract

In this work, the traditional third-order Active Flux advection scheme is modified by reformulating the method and introducing additional parameters. The effect of these parameters is studied, leading to schemes with improved dissipative properties. These improvements are validated by numerical experiments.