Two Decades of Wave-Like Equation for the Numerical Simulation of Incompressible Viscous Flow: A Review

  • Roland GlowinskiEmail author
  • Tsorng-Whay Pan
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 47)


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.


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



The authors of this article are thanking the editors of this volume, a very special thank being due to Marja-Leena Rantalainen, from the University of Jyväskylä in Finland, for her beautiful processing of this contribution. The support of the US National Science Foundation via grant DMS-1418308 is also acknowledged.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Department of MathematicsHong-Kong Baptist UniversityKowloon TongHong Kong

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