Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry

Cliffe, Andrew; Hall, Edward; Houston, Paul; Phipps, Eric; Salinger, Andrew

Abstract

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork bifurcation occurs when the underlying physical system possesses rotational and reflectional or O(2) symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual Weighted Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented. Here, particular attention is devoted to the problem of flow through a cylindrical pipe with a sudden expansion, which represents a notoriously difficult computational problem.

Citation

Cliffe, A., Hall, E., Houston, P., Phipps, E., & Salinger, A. (2012). Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry. Journal of Scientific Computing, 52(1), 153-179. https://doi.org/10.1007/s10915-011-9545-8

• Journal Article Type: Article
• Acceptance Date: Sep 16, 2011
• Online Publication Date: Oct 14, 2011
• Publication Date: 2012-07
• Deposit Date: Feb 14, 2011
• Publicly Available Date: Oct 14, 2011
• Journal: Journal of Scientific Computing
• Print ISSN: 0885-7474
• Electronic ISSN: 1573-7691
• Publisher: Springer Verlag
• Peer Reviewed: Not Peer Reviewed
• Volume: 52
• Issue: 1
• Pages: 153-179
• DOI: https://doi.org/10.1007/s10915-011-9545-8
• Keywords: Theoretical Computer Science; General Engineering; Computational Theory and Mathematics; Software
• Public URL: https://nottingham-repository.worktribe.com/output/1008488
• Publisher URL: http://link.springer.com/content/pdf/10.1007%2Fs10915-011-9545-8.pdf
• Additional Information: The final publication is available at link.springer.com