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Isogeometric Compatible Discretizations for Viscous Incompressible Flow

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

Abstract

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.

Keywords

Strouhal Number Isogeometric Analysis Incompressibility Constraint Euler Flow Hilbert Complex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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