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A Penalty Method for the Vorticity–Velocity Formulation

✍ Scribed by James Trujillo; George Em Karniadakis

Book ID
102583354
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
352 KB
Volume
149
Category
Article
ISSN
0021-9991

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✦ Synopsis

We present a new vorticity-velocity formulation and implementation for the unsteady three-dimensional Navier-Stokes equations, based on a penalty method. It relies on an equivalence theorem that employs exact boundary conditions and the vorticity definition on the domain boundary. This approach is particularly attractive for high-order methods for which the often-used influence matrix method fails to converge for t → 0. The accuracy and the robustness of the new method is demonstrated in the context of several spectral element simulations of unsteady two-and three-dimensional internal and external flows. In particular, the flow past a finite span cylinder attached to end-plates is studied in some detail in order to evaluate the effects of the aspect ratio on the formation length.

📜 SIMILAR VOLUMES

Vorticity–velocity–pressure formulation
Vorticity–velocity–pressure formulation for the Stokes problem
✍ François Dubois 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 228 KB

## Abstract We present a new variational formulation of Stokes problem of fluid mechanics that allows to take into account very general boundary conditions for velocity, tangential vorticity or pressure. This formulation conducts a well posed mathematical problem in a family of particular cases. Co