English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper, we propose a unified numerical framework for thetime-dependent incompressible Navier--Stokes equation which yields the $H^1$-,$H(\text{div})$-conforming, and discontinuous Galerkin methods with the use ofdifferent viscous stress tensors and penalty terms for pressure robustness.Under minimum assumption on Galerkin spaces, the semi- and fully-discretestability is proved when a family of implicit Runge--Kutta methods are used fortime discretization. Furthermore, we present a unified discussion on thepenalty term. Numerical experiments are presented to compare our schemes withclassical schemes in the literature in both unsteady and steady situations. Itturns out that our scheme is competitive when applied to well-known benchmarkproblems such as Taylor--Green vortex, Kovasznay flow, potential flow, liddriven cavity flow, and the flow around a cylinder.

A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier--Stokes equation