A Lagrangian Fractional Step Method for the Incompressible Navier-Stokes Equations: October 1985 (Classic Reprint) - Hardcover

Christoph Borgers

9780266772712: A Lagrangian Fractional Step Method for the Incompressible Navier-Stokes Equations: October 1985 (Classic Reprint)

Hardcover

ISBN 10: 0266772714 ISBN 13: 9780266772712

Publisher: Forgotten Books, 2018

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A practical, in-depth look at a Lagrangian approach to incompressible Navier–Stokes equations

This monograph introduces a fractional step method that adapts Peskin’s ideas to periodic domains, using Voronoi diagrams and Lagrangian markers to handle fluid flow and immersed boundaries with improved efficiency. The text explains how to discretize operators on irregular grids, employ multigrid techniques, and implement a two-level iteration to solve Helmholtz and Poisson problems at each time step. It also covers projecting velocity fields to a divergence-free state and analyzes numerical results that compare this method to traditional Eulerian approaches.

Learn how Voronoi diagrams and Monotonic Logical Grids are used to construct and update fluid meshes.
See how a two-level, implicit scheme reduces computational effort while maintaining stability and accuracy.
Understand how immersed boundaries, represented by chains of Lagrangian particles, interact with the fluid through a projection-based framework.
Review numerical experiments that illustrate convergence behavior, grid-size effects, and practical considerations for large-scale simulations.

Ideal for readers of computational fluid dynamics and numerical methods who want a rigorous, implementation-focused treatment of Lagrangian strategies for incompressible flows.

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About the Author

Christoph Borgers has been a Professor in the Department of Mathematics at Tufts University since 1994. He has also worked at the University of Michigan and at the IBM T. J. Watson Research Center. He received his PhD from New York University.

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