Some new properties of an Active flux type scheme: PamPa

TL;DR

This paper explores new theoretical properties of Active Flux and Pampa schemes, including their relation to DG schemes, bound preservation, and SBP property, supported by numerical illustrations.

Contribution

It reveals that Pampa schemes can be interpreted with DG schemes as building blocks, and establishes intrinsic bound-preserving and SBP properties.

Findings

Pampa schemes can be interpreted using DG schemes.

Intrinsic bound-preserving properties are demonstrated.

Pampa scheme exhibits SBP property in one dimension.

Abstract

In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (\pampa) schemes. First, we show, in full generality, that the AF/pampa schemes can be interpreted in such a way that the discontinuous Galerkin (dG) scheme is one of their building blocks. Secondly we provide intrinsic bound preserving properties of the current variant of pampa. This is also illustrated numerically. Last, we show, at least in one dimension, that the pampa scheme has the summation by part (SBP) property.