Dynamic p-enrichment schemes for multicomponent reactive flows

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.Comment: 29 pages, 7 figures, 3 table

Improving predictions of coastal flooding via sub-mesh corrections

ADCIRC (ADvanced CIRCulation) is a hydrodynamic model used to predict coastal water levels. During storm events, such as hurricanes, ADCIRC forecasts flood levels along the coast, which can be used to advise emergency managers and the general public and prepare them for the storm. Although ADCIRC can be highly accurate, its accuracy depends on its “mesh”, which represents the coastal environment with bathymetric elevations and bottom frictions. Meshes of high resolution and accuracy can predict water levels very precisely; however, this precision comes at a high computational cost, which delays the ability to forecast the storm and advise interested parties. This study aims to incorporate high resolution data on a lesser resolved mesh by incorporating correction factors into the governing equations. These correction factors will maintain model accuracy while also decreasing run time. This concept was applied to both 1D and 2D versions of ADCIRC, and produced stable results that mimicked the traditional version of ADCIRC.ADCIRC (ADvanced CIRCulation) is a hydrodynamic model used to predict coastal water levels. During storm events, such as hurricanes, ADCIRC forecasts flood levels along the coast, which can be used to advise emergency managers and the general public and prepare them for the storm. Although ADCIRC can be highly accurate, its accuracy depends on its “mesh”, which represents the coastal environment with bathymetric elevations and bottom frictions. Meshes of high resolution and accuracy can predict water levels very precisely; however, this precision comes at a high computational cost, which delays the ability to forecast the storm and advise interested parties. This study aims to incorporate high resolution data on a lesser resolved mesh by incorporating correction factors into the governing equations. These correction factors will maintain model accuracy while also decreasing run time. This concept was applied to both 1D and 2D versions of ADCIRC, and produced stable results that mimicked the traditional version of ADCIRC