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Related Experiment Videos

A fast, high resolution, second-order central scheme for incompressible flows.

R Kupferman1, E Tadmor

  • 1Mathematics Department, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, 50A-2152, Berkeley, CA 94720, USA.

Proceedings of the National Academy of Sciences of the United States of America
|May 13, 1997
PubMed
Summary

A new high-resolution numerical method accurately simulates incompressible flows using a second-order central difference scheme and a discrete Hodge projection. This efficient and generalizable method avoids spurious vorticity patterns, even in underresolved simulations.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Analysis
  • Applied Mathematics

Background:

  • Incompressible flow simulations require high-resolution numerical methods.
  • Existing methods may struggle with accuracy and efficiency.
  • The Lax-Friedrichs scheme is a foundational method for hyperbolic conservation laws.

Purpose of the Study:

  • To present a novel, high-resolution, second-order central difference method for incompressible flows.
  • To introduce an exact discrete Hodge projection for improved accuracy.
  • To demonstrate the method's efficiency, ease of implementation, and generalizability.

Main Methods:

  • A second-order extension of the Lax-Friedrichs scheme.
  • A new discrete Hodge projection for incompressible flows.

Related Experiment Videos

  • Testing on the standard periodic double shear-layer problem.

    • Main Results:

    • The method achieves high resolution with a compact stencil.
    • No spurious vorticity patterns were observed, even in underresolved flow conditions.
    • The scheme is computationally fast and easy to implement.

    Conclusions:

    • The presented method offers an accurate and efficient approach for simulating incompressible flows.
    • The discrete Hodge projection enhances the scheme's performance.
    • The method is robust and applicable to various fluid dynamics problems.