Mimetic Spectral Element advection

TL;DR

This paper introduces a spectral element discretization for linear advection of differential forms, extending previous frameworks to include the Lie derivative, achieving spectral accuracy and local mass conservation.

Contribution

It extends existing discretization methods by incorporating the Lie derivative via Cartan's formula, providing a physics-compatible spectral scheme with proven convergence.

Findings

Spectral convergence achieved in the discretization.

Method ensures local mass conservation.

Artificial dispersion influenced by time integration order.

Abstract

We present a discretization of the linear advection of differential forms on bounded domains. The framework previously established is extended to incorporate the Lie derivative, $\mathcal L$, by means of Cartan's homotopy formula. The method is based on a physics-compatible discretization with spectral accuracy . It will be shown that the derived scheme has spectral convergence with local mass conservation. Artificial dispersion depends on the order of time integration.