𝔖 Bobbio Scriptorium
✦   LIBER   ✦

High-order finite difference schemes for incompressible flows

✍ Scribed by H. Fadel; M. Agouzoul; P. K. Jimack

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
320 KB
Volume
65
Category
Article
ISSN
0271-2091

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper presents a new high‐order approach to the numerical solution of the incompressible Stokes and Navier–Stokes equations. The class of schemes developed is based upon a velocity–pressure–pressure gradient formulation, which allows: (i) high‐order finite difference stencils to be applied on non‐staggered grids; (ii) high‐order pressure gradient approximations to be made using standard Padé schemes, and (iii) a variety of boundary conditions to be incorporated in a natural manner. Results are presented in detail for a selection of two‐dimensional steady‐state test problems, using the fourth‐order scheme to demonstrate the accuracy and the robustness of the proposed methods. Furthermore, extensions to higher orders and time‐dependent problems are illustrated, whereas the extension to three‐dimensional problems is also discussed. Copyright © 2010 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

Fully Conservative Higher Order Finite D
Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow
✍ Y. Morinishi; T.S. Lund; O.V. Vasilyev; P. Moin 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 451 KB

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation

HIGH-ORDER-ACCURATE SCHEMES FOR INCOMPRE
HIGH-ORDER-ACCURATE SCHEMES FOR INCOMPRESSIBLE VISCOUS FLOW
✍ John C. Strikwerda 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 191 KB 👁 1 views

We present new finite difference schemes for the incompressible Navier-Stokes equations. The schemes are based on two spatial differencing methods; one is fourth-order-accurate and the other is sixth-order accurate. The temporal differencing is based on backward differencing formulae. The schemes us

Finite Difference Schemes for Incompress
Finite Difference Schemes for Incompressible Flows in the Velocity–Impulse Density Formulation
✍ Weinan E; Jian-Guo Liu 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 434 KB

together with perspectives on the application of real space renormalization procedures to vortex methods based on We consider finite difference schemes based on the impulse density variable. We show that the original velocity-impulse density the impulse density. formulation of Oseledets is margina

A Fully Conservative Second-Order Finite
A Fully Conservative Second-Order Finite Difference Scheme for Incompressible Flow on Nonuniform Grids
✍ F.E. Ham; F.S. Lien; A.B. Strong 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 150 KB

A second-order-accurate finite difference discretization of the incompressible Navier-Stokes is presented that discretely conserves mass, momentum, and kinetic energy (in the inviscid limit) in space and time. The method is thus completely free of numerical dissipation and potentially well suited to

A high order finite element for complete
A high order finite element for completely incompressible creeping flow
✍ Erik G. Thompson; M. I. Haque 📂 Article 📅 1973 🏛 John Wiley and Sons 🌐 English ⚖ 359 KB

## Abstract A finite element method for simulating the creeping flow of an incompressible material is presented. The method allows for (1) a quadratic approximation of the velocity field, (2) material incompressibility everywhere within an element and (3) the ability to follow the flow through larg