An ‘assumed deviatoric stress‐pressure‐velocity’ mixed finite element method for unsteady, convective, incompressible viscous flow: Part II: Computational studies

Chien‐Tung ‐T Yang, Satya N. Atluri

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

In Part I of this paper we presented a mixed finite element method, for solving unsteady, incompressible, convective flows, based on assumed ‘deviatoric stress–velocity–pressure’ fields in each element, which have the features: (i) the convective term is treated by the usual Galerkin technique; (ii) the unknowns in the global system of finite element equations are the nodal velocities, and the ‘constant term’ in the arbitrary pressure field over each element; and (iii) exact integrations are performed over each element. In this paper we present numerical studies, both for steady as well as unsteady cases, of the problems: (a) the driven cavity, (b) Jeffry–Hamel flow in a channel, (c) flow over a ‘backward’ or ‘downstream’ facing step, and (d) flow over a square step. All these problems are two‐dimensional in nature, although certain 3‐D solutions are to be presented in a separate paper. The present results are compared with those which are available in the literature and are based on alternative approaches to treat incompressibility and convective acceleration. The possible merits of the present method are thus pointed out.

Original languageEnglish
Pages (from-to)43-69
Number of pages27
JournalInternational Journal for Numerical Methods in Fluids
Volume4
Issue number1
DOIs
StatePublished - Jan 1984

Keywords

  • Assumed Deviatoric Stress
  • Galerkin Formulation
  • Mixed Method

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