Pseudo-divergence-free element free Galerkin method for incompressible fluid flow

Author (s): Huerta, A., Vidal, Y. and Villon, P.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 193, Issue 12 – 14
Pages: 1119 – 1136
Date: 2004

Incompressible modelling in finite elements has been a major concern since its early developments and has been extensively studied. However, incompressibility in mesh-free methods is still an open topic. Thus, instabilities or locking can preclude the use of mesh-free approximations in such problems. Here, a novel mesh-free formulation is proposed for incompressible flow. It is based on defining a pseudo-divergence-free interpolation space. That is, the finite dimensional interpolation space approaches a divergence-free space when the discretization is refined. Note that such an interpolation does not include any overhead in the computations. The numerical evaluations are performed using the inf-sup numerical test and two well-known benchmark examples for Stokes flow.



  Author   = {Huerta, Antonio and Vidal, Yolanda and Villon, Pierre},
  Title    = {Pseudo-divergence-free element free {G}alerkin method for incompressible fluid flow},
  Fjournal = {Computer Methods in Applied Mechanics and Engineering},
  Journal  = {Comput. Methods Appl. Mech. Eng.},
  Volume   = {193},
  Number   = {12--14},
  Pages    = {1119--1136},
  Year     = {2004}}