H-1 Least Squares Method for the Navier-Stokes Equations

Roland Glowinski*, B. Mantel, J. Periaux, O. Pironneau

*Corresponding author for this work

Research output: Contribution to conferenceConference paperpeer-review

3 Citations (Scopus)


Separated incompressible viscous flows around wings and airfoils are simulated by the numerical solution of the unsteady Navier-Stokes equations at low Reynolds number. The nonlinear equations are minimized in the Sobolev-Space H** minus **1 ( OMEGA ). It is shown that this method amounts to a sequence of optimal control problems with the Stokes equations as dynamics (state system). A fast solver is used for the Stokes equations based on a new mixed formulation. The formulation is discretized in finite elements. The mixed formulation can be decomposed into elementary standard Dirichlet problems. The optimal control problem is solved by a conjugate gradient method. Thus, although the method is fully implicit in time, it amounts to solving a few Dirichlet equations at each iteration.

Original languageEnglish
Number of pages14
Publication statusPublished - 1978
EventNumer Methods in Laminar and Turbul Flow, Proc of the Int Conf, 1st - Swansea, Wales
Duration: 17 Jul 197821 Jul 1978


ConferenceNumer Methods in Laminar and Turbul Flow, Proc of the Int Conf, 1st
CitySwansea, Wales

Scopus Subject Areas

  • Engineering(all)


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