Control Theory based Shape Design for the Incompressible Navier-Stokes Equations

G. Cowles, Luigi Martinelli

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A design method for shape optimization in incompressible turbulent viscous flow has been developed and validated for inverse design. The gradient information is determined using a control theory based algorithm. With such an approach, the cost of computing the gradient is negligible. An additional adjoint system must be solved which requires the cost of a single steady state flow solution. Thus, this method has an enormous advantage over traditional finite-difference based algorithms. The method of artificial compressibility is utilized to solve both the flow and adjoint systems. An algebraic turbulence model is used to compute the eddy viscosity. The method is validated using several inverse wing design test cases. In each case, the program must modify the shape of the initial wing such that its pressure distribution matches that of the target wing. Results are shown for the inversion of both finite thickness wings as well as zero thickness wings which can be considered a model of yacht sails.

Original languageEnglish (US)
Pages (from-to)499-514
Number of pages16
JournalInternational Journal of Computational Fluid Dynamics
Issue number6
StatePublished - Dec 1 2003

All Science Journal Classification (ASJC) codes

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


  • Adjoint
  • Incompressible
  • Navier-Stokes
  • RANS
  • Sails
  • Shape design


Dive into the research topics of 'Control Theory based Shape Design for the Incompressible Navier-Stokes Equations'. Together they form a unique fingerprint.

Cite this