Higher order spectral/hp finite element models of the Navier-Stokes equations

V. P. Vallalaa, Reza Sadr, J. N. Reddy

Research output: Contribution to journalArticle

5 Citations (Scopus)


In this paper, we present higher order least-squares finite element formulations for viscous, incompressible, isothermal Navier-Stokes equations using spectral/hp basis functions. The second-order Navier-Stokes equations are recast as first-order system of equations using stresses as auxiliary variables. Both steady-state and transient problems are considered. For a better coupling of pressure and velocity, especially in transient flows, an iterative penalisation strategy is employed. The outflow-type boundary conditions are applied in a weak sense through the least-squares functional. The formulation is verified by solving various benchmark problems like the lid-driven cavity, backward-facing step and flow over cylinder problems using direct serial solver UMFPACK.

Original languageEnglish
Pages (from-to)16-30
Number of pages15
JournalInternational Journal of Computational Fluid Dynamics
Issue number1-2
Publication statusPublished - 2014



  • first-order formulations
  • higher order finite elements
  • least-squares formulations
  • Navier-Stokes equations
  • spectral/hp methods

ASJC Scopus subject areas

  • Computational Mechanics
  • Aerospace Engineering
  • Condensed Matter Physics
  • Energy Engineering and Power Technology
  • Mechanics of Materials
  • Mechanical Engineering

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