Least-squares spectral element solution of incompressible Navier-Stokes equations with adaptive refinement


Ozcelikkale A., SERT C.

JOURNAL OF COMPUTATIONAL PHYSICS, vol.231, no.9, pp.3755-3769, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 231 Issue: 9
  • Publication Date: 2012
  • Doi Number: 10.1016/j.jcp.2012.01.024
  • Journal Name: JOURNAL OF COMPUTATIONAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.3755-3769
  • Keywords: Least-squares, Spectral element method, Incompressible flow, Adaptive refinement, Constrained Approximation Method, MASS-CONSERVATION, FORMULATIONS, FLOWS, MOMENTUM

Abstract

Least-squares spectral element solution of steady, two-dimensional, incompressible flows are obtained by approximating velocity, pressure and vorticity variable set on GaussLobatto-Legendre nodes. Constrained Approximation Method is used for h- and p-type nonconforming interfaces of quadrilateral elements. Adaptive solutions are obtained using a posteriori error estimates based on least squares functional and spectral coefficient. Effective use of p-refinement to overcome poor mass conservation drawback of leastsquares formulation and successful use of h- and p-refinement together to solve problems with geometric singularities are demonstrated. Capabilities and limitations of the developed code are presented using Kovasznay flow, flow past a circular cylinder in a channel and backward facing step flow. (C) 2012 Elsevier Inc. All rights reserved.