Skip to main content

Meshless Methods

  • Reference work entry
  • 308 Accesses

Synonyms

Meshfree methods; Element-free methods; Particle methods

Definition

Meshless methods belong to a class of techniques for solving boundary/initial value partial differential equations in which both geometry representation and numerical discretization are principally performed based on nodes or particles. In meshless methods, there is no inherent reliance on a particular mesh topology meaning that no element connectivity is required. In practice, however, in many meshless methods recourse must be taken to some kind of background meshes at least in one stage of the implementation.

Overview

Analysis of many practical processes in modern engineering requires modeling of problems with time dependent geometry or boundary conditions. Pulsating flow of blood in heart, metal forming processes and stretching of a polymer filament are only a few examples. Conventional mesh based methods such as the Finite Volume and Finite Element Methods face serious difficulties when dealing with...

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-0-387-48998-8_885
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   1,299.00
Price excludes VAT (USA)
  • ISBN: 978-0-387-48998-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Figure 1
Figure 2
Figure 3
Figure 4

References

  1. Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astrono J 82(12):1013–1024

    Google Scholar 

  2. Gingold RA, Monaghan JJ (1977) Smoothed Particle Hydrodynamics: theory and application to non-spherical stars. Mon Not Roy Astron Soc 181(2):375–389

    MATH  Google Scholar 

  3. Liu GR (2003) Mesh Free Methods: Moving beyond the finite element method. CRC Press, Boca Raton

    MATH  Google Scholar 

  4. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: An Overview and Recent Developments. Comp Meth Appl Mech Engin 139(1–4):3–47

    MATH  Google Scholar 

  5. Koumoutsakos P (2005) Multiscale Flow Simulations using Particles. Annu Rev Fluid Mech 37:457–487

    MathSciNet  Google Scholar 

  6. Babuska I, Banerjee U, Osborn JE (2002) Survey of Meshless and Generalized Finite Element Methods: A Unified Approach. TICAM Report 02–40, University of Texas at Austin

    Google Scholar 

  7. Gavete L, Gavete ML, Benito JJ (2003) Improvements of generalized finite difference method and comparison with other meshless method. Appl Math Model 27:831–847

    MATH  Google Scholar 

  8. Monaghan JJ (1992) Smoothed Particle Hydrodynamics. Ann Rev Astron Astrophys 30:543–574

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Manzari, M. (2008). Meshless Methods. In: Li, D. (eds) Encyclopedia of Microfluidics and Nanofluidics. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-48998-8_885

Download citation