Two decades of wave-like equation for the numerical simulation of incompressible viscous flow: A review

Roland GLOWINSKI*, Tsorng Whay Pan

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review

4 Citations (Scopus)


A wave-like equation based method for the numerical solution of the Navier-Stokes equations modeling incompressible viscous flow was introduced nearly twenty years ago. From its inception to nowadays it has been applied successfully to the numerical solution of two and three dimensional flow problems for incompressible Newtonian and non-Newtonian viscous fluids, in flow regions with fixed or moving boundaries. The main goals of this article are: (i) To recall the foundations of the wave-like equation methodology, and (ii) to review some typical viscous flow problems where it has been applied successfully.

Original languageEnglish
Title of host publicationContributions to Partial Differential Equations and Applications
EditorsB. N. Chetverushkin, W. Fitzgibbon, Y.A. Kuznetsov, P. Neittaanmäki, J. Periaux, O. Pironneau
PublisherSpringer Cham
Number of pages30
ISBN (Electronic)9783319783253
ISBN (Print)9783319783246, 9783030086756
Publication statusPublished - 20 Jul 2018

Publication series

NameComputational Methods in Applied Sciences
ISSN (Print)1871-3033

Scopus Subject Areas

  • Civil and Structural Engineering
  • Modelling and Simulation
  • Biomedical Engineering
  • Computer Science Applications
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Electrical and Electronic Engineering

User-Defined Keywords

  • Finite element approximations
  • Incompressible viscous flow
  • Operator splitting time discretization schemes
  • Wave-like equation method for the numerical treatment of the advection step


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