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Numerical vorticity creation based on impulse conservation.

D M Summers1, A J Chorin

  • 1Mathematics Department, Napier University, Edinburgh, Scotland.

Proceedings of the National Academy of Sciences of the United States of America
|March 5, 1996
PubMed
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Lagrangian vortex methods now satisfy no-slip boundary conditions using impulse elements. This approach converts wall impulses into vortex loops, advancing numerical fluid dynamics simulations.

Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Vortex dynamics

Background:

  • Lagrangian vortex methods are crucial for simulating fluid flows.
  • Satisfying no-slip boundary conditions in these methods presents a significant challenge.
  • Existing methods often struggle with accurate boundary condition implementation.

Purpose of the Study:

  • To resolve the challenge of creating solenoidal vortex elements for no-slip boundary conditions in Lagrangian numerical vortex methods.
  • To introduce a novel algorithm utilizing impulse elements at walls.
  • To explore the conversion of these impulse elements into vortex loops.

Main Methods:

  • The study employs impulse elements applied at boundaries to represent wall interactions.
  • These impulse elements are subsequently converted into solenoidal vortex loops.

Related Experiment Videos

  • The research discusses two distinct gauge choices within the impulse definition, acknowledging gauge freedom.

    • Main Results:

    • A viable method for imposing no-slip boundary conditions in Lagrangian vortex methods is presented.
    • The conversion of impulse elements to vortex loops effectively addresses the boundary condition problem.
    • The algorithm's non-unique nature due to gauge freedom is identified, with optimal gauge choice remaining an open question.

    Conclusions:

    • The proposed method offers a robust solution for incorporating no-slip boundary conditions in Lagrangian vortex simulations.
    • Further research is needed to determine the numerically optimal gauge for impulse definition.
    • The approach shows potential for applications such as flow past a sphere.