The University of Southampton
University of Southampton Institutional Repository

An axis treatment for flow equations in cylindrical coordinates based on parity conditions

An axis treatment for flow equations in cylindrical coordinates based on parity conditions
An axis treatment for flow equations in cylindrical coordinates based on parity conditions
A novel axis treatment using parity conditions is presented for flow equations in cylindrical coordinates that are represented in azimuthal Fourier modes. The correct parity states of scalars and the velocity vector are derived such that symmetry conditions for each Fourier mode of the respective variable can be determined. These symmetries are then used to construct finite-difference and filter stencils at and near the axis, and an interpolation scheme for the computation of terms premultiplied by 1/r. A grid convergence study demonstrates that the axis treatment retains the formal accuracy of the spatial discretization scheme employed. Two further test cases are considered for evaluation of the axis treatment, the propagation of an acoustic pulse and direct numerical simulation of a fully turbulent supersonic axisymmetric wake. The results demonstrate the applicability of the axis treatment for non-axisymmetric flows
polar coordinate singularity, navier–stokes equations, euler equations, direct numerical simulation, axis treatment, cylindrical coordinates
0045-7930
166-172
Sandberg, Richard D.
41d03f60-5d12-4f2d-a40a-8ff89ef01cfa
Sandberg, Richard D.
41d03f60-5d12-4f2d-a40a-8ff89ef01cfa

Sandberg, Richard D. (2011) An axis treatment for flow equations in cylindrical coordinates based on parity conditions. Computers & Fluids, 49 (1), 166-172. (doi:10.1016/j.compfluid.2011.05.009).

Record type: Article

Abstract

A novel axis treatment using parity conditions is presented for flow equations in cylindrical coordinates that are represented in azimuthal Fourier modes. The correct parity states of scalars and the velocity vector are derived such that symmetry conditions for each Fourier mode of the respective variable can be determined. These symmetries are then used to construct finite-difference and filter stencils at and near the axis, and an interpolation scheme for the computation of terms premultiplied by 1/r. A grid convergence study demonstrates that the axis treatment retains the formal accuracy of the spatial discretization scheme employed. Two further test cases are considered for evaluation of the axis treatment, the propagation of an acoustic pulse and direct numerical simulation of a fully turbulent supersonic axisymmetric wake. The results demonstrate the applicability of the axis treatment for non-axisymmetric flows

Full text not available from this repository.

More information

e-pub ahead of print date: 26 May 2011
Published date: October 2011
Keywords: polar coordinate singularity, navier–stokes equations, euler equations, direct numerical simulation, axis treatment, cylindrical coordinates
Organisations: Aeronautics, Astronautics & Comp. Eng, Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 300806
URI: http://eprints.soton.ac.uk/id/eprint/300806
ISSN: 0045-7930
PURE UUID: 8fd54e71-c83c-4fde-a699-54df43746e7d
ORCID for Richard D. Sandberg: ORCID iD orcid.org/0000-0001-5199-3944

Catalogue record

Date deposited: 29 Feb 2012 12:23
Last modified: 02 Dec 2019 20:59

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×