Implementation of A Least Squares Method To A Navier-Stokes Solver

The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares solver to the lid driven cavity problem and discuss results

Extinction Risk and Diversification Are Linked in a Plant Biodiversity Hotspot

Plant extinction risks in the Cape, South Africa differ from those for vertebrates worldwide, with young and fast-evolving plant lineages marching towards extinction at the fastest rate, but independently of human effects

The noise-lovers: cultures of speech and sound in second-century Rome

This chapter provides an examination of an ideal of the ‘deliberate speaker’, who aims to reflect time, thought, and study in his speech. In the Roman Empire, words became a vital tool for creating and defending in-groups, and orators and authors in both Latin and Greek alleged, by contrast, that their enemies produced babbling noise rather than articulate speech. In this chapter, the ideal of the deliberate speaker is explored through the works of two very different contemporaries: the African-born Roman orator Fronto and the Syrian Christian apologist Tatian. Despite moving in very different circles, Fronto and Tatian both express their identity and authority through an expertise in words, in strikingly similar ways. The chapter ends with a call for scholars of the Roman Empire to create categories of analysis that move across different cultural and linguistic groups. If we do not, we risk merely replicating the parochialism and insularity of our sources.Accepted manuscrip