𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New subgrid artificial viscosity Galerkin methods for the Navier–Stokes equations

✍ Scribed by Keith J. Galvin

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
870 KB
Volume
200
Category
Article
ISSN
0045-7825

No coin nor oath required. For personal study only.

✦ Synopsis

We study subgrid artificial viscosity methods for approximating solutions to the Navier-Stokes equations. Two methods are introduced that add viscous stabilization via an artificial viscosity, then remove it only on a coarse mesh. These methods can be considered as conforming, mixed methods, the first for velocity and vorticity, and the second for velocity and its gradient, the former incorporating a naturally arising grad-div stabilization term. In this paper, we rigorously study the first scheme analytically, showing that it is unconditionally stable and optimally convergent, as well as both schemes computationally. Numerical experiments demonstrate the advantages of both of these methods.

📜 SIMILAR VOLUMES

A discontinuous Galerkin method for the
A discontinuous Galerkin method for the Navier–Stokes equations
✍ Igor Lomtev; George Em Karniadakis 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 526 KB

The foundations of a new discontinuous Galerkin method for simulating compressible viscous flows with shocks on standard unstructured grids are presented in this paper. The new method is based on a discontinuous Galerkin formulation both for the advective and the diffusive contributions. High-order

Discontinuous Galerkin methods for the N
Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations
✍ A. Montlaur; S. Fernandez-Mendez; J. Peraire; A. Huerta 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 254 KB 👁 2 views

## Abstract An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high‐order piecewise divergence‐free approximations, leading to t

Nonlinear Galerkin method and two-step m
Nonlinear Galerkin method and two-step method for the Navier-Stokes equations
✍ He Yinnian; Li Kaitai 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 666 KB

This article represents a new nonlinear Galerkin scheme for the Navier-Stokes equations. This scheme consists of a nonlinear Galerkin finite element method and a two-step difference method. Moreover, we also provide a Galerkin scheme. By convergence analysis, two numerical schemes have the same seco