On the integral constraint of the pressure Poisson equation for incompressible flows

We illustrate, using analytical and numerical proofs, how a conservative discretisation of the pressure Poisson equation arising out of the discretisation of the incompressible Navier-Stokes equations (on a two-dimensional unstructured non-staggered grid) satisfies the integral constraint on the pre...

Full description

Saved in:
Bibliographic Details
Published inInternational journal of computational fluid dynamics Vol. 26; no. 9-10; pp. 489 - 498
Main Authors Chandar, Dominic, Sitaraman, Jayanarayanan, Mavriplis, Dimitri J.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.10.2012
Taylor & Francis Ltd
Subjects
Boundary conditions
finite volume methods
Fluid dynamics
incompressible Navier-Stokes equations
integral constraint
Integrals
iterative methods
Poisson distribution
Pressure
pressure Poisson formulation
Online AccessGet full text

Cover

More Information
Summary:We illustrate, using analytical and numerical proofs, how a conservative discretisation of the pressure Poisson equation arising out of the discretisation of the incompressible Navier-Stokes equations (on a two-dimensional unstructured non-staggered grid) satisfies the integral constraint on the pressure boundary condition without any additional treatment. When discretised in a non-conservative manner, it is seen that the integral constraint is not exactly satisfied, but only to an order , where is an appropriate velocity scale. When solved using an iterative method, such as the Bi-Conjugate Stabilised method, it is proved that the vanishing sum of residuals on all points inclusive of the boundary is a consequence of this integral constraint. This result can then be used as a tool to identify whether the discrete integral constraint has been satisfied or not, especially when the pressure is solved as a Neumann problem.
ISSN:1061-8562
1029-0257
DOI:10.1080/10618562.2012.723127