Velocity–pressure integrated versus penalty finite element methods for high‐Reynolds‐number flows

S. ‐W Kim, Rand A. Decker

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Velocity–pressure integrated and consistent penalty finite element computations of high‐Reynolds‐number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity‐pressure integrated method, yields accurate computational results for high‐Reynolds‐number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity–pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid‐driven cavity flow of Reynolds number 10 000, a laminar backward‐facing step flow and a laminar flow through a nest of cylinders.

Original languageEnglish (US)
Pages (from-to)43-57
Number of pages15
JournalInternational Journal for Numerical Methods in Fluids
Issue number1
StatePublished - Jan 1989


  • Consistent penalty
  • Finite element
  • Penalty method

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


Dive into the research topics of 'Velocity–pressure integrated versus penalty finite element methods for high‐Reynolds‐number flows'. Together they form a unique fingerprint.

Cite this