Dynamic p-enrichment schemes for multicomponent reactive flows

TL;DR

This paper introduces a family of p-enrichment schemes for multicomponent reactive flows, distinguishing between fixed tolerance and dioristic schemes, tested on coastal hydrology models to improve stability and accuracy.

Contribution

It proposes novel p-enrichment schemes with two classes and types, enhancing solution stability and accuracy in reactive flow simulations.

Findings

Fixed tolerance schemes rely on global scalar tolerances.

Dioristic schemes use time-evolving bounds on local variation.

Schemes tested on contaminant transport and eutrophication models.

Abstract

We present a family of p-enrichment schemes. These schemes may be separated into two basic classes: the first, called \emph{fixed tolerance schemes}, rely on setting global scalar tolerances on the local regularity of the solution, and the second, called \emph{dioristic schemes}, rely on time-evolving bounds on the local variation in the solution. Each class of $p$-enrichment scheme is further divided into two basic types. The first type (the Type I schemes) enrich along lines of maximal variation, striving to enhance stable solutions in "areas of highest interest." The second type (the Type II schemes) enrich along lines of maximal regularity in order to maximize the stability of the enrichment process. Each of these schemes are tested over a pair of model problems arising in coastal hydrology. The first is a contaminant transport model, which addresses a declinature problem for a contaminant plume with respect to a bay inlet setting. The second is a multicomponent chemically reactive flow model of estuary eutrophication arising in the Gulf of Mexico.