Isogeometric Compatible Discretizations for Viscous Incompressible Flow

  • John A. EvansEmail author
  • Thomas J. R. Hughes
Part of the Lecture Notes in Mathematics book series (LNM, volume 2161)


In this chapter, isogeometric discretizations for viscous incompressible flow are presented that satisfy the incompressibility constraint in a pointwise manner. As incompressibility is satisfied pointwise, these discretizations replicate the geometric structure of the Navier-Stokes equations and properly balance energy, enstrophy, and helicity. The result is a method with enhanced accuracy and robustness as compared with classical finite element methods for incompressible flow. Within the chapter, we review the geometric structure of the Navier-Stokes equations, outline the construction of compatible B-spline spaces which allow for pointwise mass conservation, and present a suite of illustrative numerical results demonstrating the potential of compatible B-splines in computational fluid dynamics.


Strouhal Number Isogeometric Analysis Incompressibility Constraint Euler Flow Hilbert Complex 
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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of Colorado BoulderBoulderUSA
  2. 2.Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA

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