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Cartesian Grid Methods for Fluid Flow in Complex Geometries

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Computational Modeling in Biological Fluid Dynamics

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 124))

Abstract

Biological fluid dynamics typically involves geometrically complicated structures which are often deforming in time. We give a brief overview of some approaches based on using fixed Cartesian grids instead of attempting to use a grid which conforms to the boundary. Both finite-difference and finite-volume methods are discussed, as well as a combined approach which has recently been used for computing incompressible flow using the streamfunction-vorticity formulation of the incompressible Navier-Stokes equations.

The work of the both authors was supported in part by DOE grant DE-FG03-96ER25292 and NSF grants DMS-9505021 and DMS-9626645.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Washington, Box 352420, Seattle, WA, 98195-2420

    Randall J. Leveque

  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY, 10012

    Donna Calhoun

Authors
  1. Randall J. Leveque
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  2. Donna Calhoun
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA

    Lisa J. Fauci

  2. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Shay Gueron

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Leveque, R.J., Calhoun, D. (2001). Cartesian Grid Methods for Fluid Flow in Complex Geometries. In: Fauci, L.J., Gueron, S. (eds) Computational Modeling in Biological Fluid Dynamics. The IMA Volumes in Mathematics and its Applications, vol 124. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0151-6_7

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  • DOI: https://doi.org/10.1007/978-1-4613-0151-6_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6539-9

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