Isogeometric Divergence-conforming B-splines for the Unsteady Navier-Stokes Equations

Abstract

Divergence-conforming B-splines are developed for application to the incompressible Navier-Stokes equations on geometrically mapped domains. These enable smooth pointwise divergence-free solutions and thus satisfy mass conservation in the strongest possible sense. Semi-discrete methods based on divergence-conforming B-splines are shown to conserve linear and angular momentum and satisfy balance laws for energy vorticity, enstrophy, and helicity. These are geometric structure-preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate. The methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2012
Accession Number
ADA560939

Entities

People

  • John Andrew Evans
  • Thomas J.R. Hughes

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Angular Momentum
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Couette Flow
  • Differential Equations
  • Engineering
  • Equations
  • Layers
  • Linear Momentum
  • Momentum
  • Navier Stokes Equations
  • Partial Differential Equations
  • Simulations
  • Stratified Fluids
  • Three Dimensional
  • Two Dimensional

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Fluid Mechanics and Fluid Dynamics.